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Relative growth of the partial sums of certain random Fibonacci-like sequencesSep 14 2017We consider certain Fibonacci-like sequences $(X_n)_{n\geq 0}$ perturbed with a random noise. Our main result is that $\frac{1}{X_n}\sum_{k=0}^{n-1}X_k$ converges in distribution, as $n$ goes to infinity, to a random variable $W$ with Pareto-like distribution ... More

A note on multitype branching processes with immigration in a random environmentMay 13 2005Aug 13 2007We consider a multitype branching process with immigration in a random environment introduced by Key in [Ann. Probab. 15 (1987) 344--353]. It was shown by Key that, under the assumptions made in [Ann. Probab. 15 (1987) 344--353], the branching process ... More

One-dimensional linear recursions with Markov-dependent coefficientsSep 19 2004Apr 03 2007For a class of stationary Markov-dependent sequences $(A_n,B_n)\in\mathbb{R}^2,$ we consider the random linear recursion $S_n=A_n+B_nS_{n-1},$ $n\in\mathbb{Z},$ and show that the distribution tail of its stationary solution has a power law decay.

Transient random walks on a strip in a random environmentMar 16 2006Jan 21 2009We consider transient random walks on a strip in a random environment. The model was introduced by Bolthausen and Goldsheid [Comm. Math. Phys. 214 (2000) 429--447]. We derive a strong law of large numbers for the random walks in a general ergodic setup ... More

A log-scale limit theorem for one-dimensional random walks in random environmentsAug 04 2004We consider a random walk X_n in non-i.i.d. environment and show that the ratio of log X_n to log n converges in probability to a positive constant.

Maximum occupation time of a transient excited random walk on ZNov 04 2011We consider a transient excited random walk on $Z$ and study the asymptotic behavior of the occupation time of a currently most visited site. In particular, our results imply that, in contrast to the random walks in random environment, a transient excited ... More

On random coefficient INAR(1) processesApr 15 2012The random coefficient integer-valued autoregressive process was introduced by Zheng, Basawa, and Datta. In this paper we study the asymptotic behavior of this model (in particular, weak limits of extreme values and the growth rate of partial sums) in ... More

Avalanches in an excitable networkApr 02 2019We study propagation of avalanches in a certain excitable network. The model is a particular case of the one introduced in [23], and is mathematically equivalent to an endemic variation of the Reed-Frost epidemic model introduced in [27]. Two types of ... More

Finite automata, probabilistic method, and occurrence enumeration of a pattern in words and permutationsMay 14 2019The main theme of this paper is the enumeration of the occurrence of a pattern in words and permutations. We mainly focus on asymptotic properties of the sequence $f_r^v(k,n),$ the number of $n$-array $k$-ary words that contain a given pattern $v$ exactly ... More

On a directionally reinforced random walkNov 04 2011We consider a generalized version of a directionally reinforced random walk, which was originally introduced by Mauldin, Monticino, and von Weizs\"{a}cker in \cite{drw}. Our main result is a stable limit theorem for the position of the random walk in ... More

Staircase patterns in words: subsequences, subwords, and separation numberAug 02 2019We revisit staircases for words and prove several exact as well as asymptotic results for longest left-most staircase subsequences and subwords and staircase separation number, the latter being defined as the number of consecutive maximal staircase subwords ... More

On ballistic deposition process on a stripMar 29 2019Jun 19 2019We revisit the model of the ballistic deposition studied in \cite{bdeposition} and prove several combinatorial properties of the random tree structure formed by the underlying stochastic process. Our results include limit theorems for the number of roots ... More

On ballistic deposition process on a stripMar 29 2019We revisit the model of the ballistic deposition studied in \cite{bdeposition} and prove several combinatorial properties of the random tree structure formed by the underlying stochastic process. Our results include limit theorems for the number of roots ... More

Random Walks in a Sparse Random EnvironmentFeb 20 2016Sep 05 2016We introduce random walks in a sparse random environment on $\mathbb Z$ and investigate basic asymptotic properties of this model, such as recurrence-transience, asymptotic speed, and limit theorems in both the transient and recurrent regimes. The new ... More

Optimal control of a stochastic network driven by a fractional Brownian motion inputAug 08 2008We consider a stochastic control model driven by a fractional Brownian motion. This model is a formal approximation to a queueing network with an on-off input process. We study stochastic control problems associated with the long-run average cost, the ... More

On the range of the transient frog model on ZFeb 09 2015In this paper we observe the frog model, an infinite system of interacting random walks, on Z with an asymmetric underlying random walk. Under the assumption of transience with a fixed frog distribution, we construct an explicit formula for the moments ... More

On a species survival modelJun 14 2010In this paper we provide some sharp asymptotic results for a stochastic model of species survival recently proposed by Guiol, Marchado, and Schinazi.

A random walk on Z with drift driven by its occupation time at zeroNov 30 2007We consider a nearest neighbor random walk on the one-dimensional integer lattice with drift towards the origin determined by an asymptotically vanishing function of the number of visits to zero. We show the existence of distinct regimes according to ... More

Height of records in partitions of a setAug 02 2019We study the restricted growth function associated with set partitions, and obtain exact formulas for the number of strong records with height one, the total of record heights over set of partitions, and the number of partitions with a given maximal height ... More

Limit theorems for one-dimensional transient random walks in Markov environmentsAug 15 2003Apr 21 2004We obtain non-Gaussian limit laws for one-dimensional random walk in a random environment assuming that the environment is a function of a stationary Markov process. This is an extension of the work of Kesten, M. Kozlov and Spitzer for random walks in ... More

Random Walks in a Sparse Random EnvironmentFeb 20 2016Nov 30 2016We introduce random walks in a sparse random environment on $\mathbb Z$ and investigate basic asymptotic properties of this model, such as recurrence-transience, asymptotic speed, and limit theorems in both the transient and recurrent regimes. The new ... More

Stable limit laws for random walk in a sparse random environment I: moderate sparsityApr 27 2018A random walk in a sparse random environment is a model introduced by Matzavinos et al. [Electron. J. Probab. 21, paper no. 72: 2016] as a generalization of both a simple symmetric random walk and a classical random walk in a random environment. A random ... More

Random walk on the Poincaré disk induced by a group of Möbius transformationsApr 17 2018We consider a discrete-time random motion, Markov chain on the Poincar\'{e} disk. In the basic variant of the model a particle moves along certain circular arcs within the disk, its location is determined by a composition of random M\"{o}bius transformations. ... More

Moran-type bounds for the fixation probability in a frequency-dependent Wright-Fisher modelSep 03 2016We study stochastic evolutionary game dynamics in a population of finite size. Individuals in the population are divided into two dynamically evolving groups. The structure of the population is formally described by a Wright-Fisher type Markov chain with ... More

A Markovian influence graph formed from utility line outage data to mitigate cascadingFeb 02 2019We use observed transmission line outage data to make a Markov influence graph that describes the probabilities of transitions between generations of cascading line outages, where each generation of a cascade consists of a single line outage or multiple ... More

Multivariate linear recursions with Markov-dependent coefficientsJun 14 2010We study a linear recursion with random Markov-dependent coefficients. In a "regular variation in, regular variation out" setup we show that its stationary solution has a multivariate regularly varying distribution. This extends results previously established ... More

On probabilistic analog automataApr 29 2003Apr 30 2003We consider probabilistic automata on a general state space and study their computational power. The model is based on the concept of language recognition by probabilistic automata due to Rabin and models of analog computation in a noisy environment suggested ... More

A Gröbner basis for Kazhdan-Lusztig idealsSep 03 2009Nov 11 2011Kazhdan-Lusztig ideals, a family of generalized determinantal ideals investigated in [Woo-Yong '08], provide an explicit choice of coordinates and equations encoding a neighbourhood of a torus-fixed point of a Schubert variety on a type A flag variety. ... More

Neutrino energy quantization in rotating mediumSep 30 2008Exact solution of the modified Dirac equation in rotating medium is found in polar coordinates in the limit of vanishing neutrino mass. The solution for the active left-handed particle exhibit properties similar to those peculiar for the charged particle ... More

General Conditions for Lepton Flavour Violation at Tree- and 1-Loop LevelSep 20 2007In this work, we compile the necessary and sufficient conditions a theory has to fulfill in order to ensure general lepton flavour conservation, in the spirit of the Glashow-Weinberg criteria for the absence of flavour-changing neutral currents. At tree-level, ... More

Discrete Uniqueness Sets for Functions with Spectral GapsSep 15 2016It is well-known that entire functions whose spectrum belongs to a fixed bounded set $S$ admit real uniformly discrete uniqueness sets $\Lambda$. We show that the same is true for much wider spaces of continuous functions. In particular, Sobolev spaces ... More

Categorical joinsMar 31 2018Mar 01 2019We introduce the notion of a categorical join, which can be thought of as a categorification of the classical join of two projective varieties. This notion is in the spirit of homological projective duality, which categorifies classical projective duality. ... More

Derived categories of Gushel-Mukai varietiesMay 21 2016Oct 25 2017We study the derived categories of coherent sheaves on Gushel-Mukai varieties. In the derived category of such a variety, we isolate a special semiorthogonal component, which is a K3 or Enriques category according to whether the dimension of the variety ... More

Automatic Kolmogorov complexity, normality and finite state dimension revisitedJan 31 2017Jul 02 2019It is well known that normality can be described as incompressibility via finite automata. Still the statement and the proof of this result as given by Becher and Heiber (2013) in terms of "lossless finite-state compressors" do not follow the standard ... More

Spectral perturbation theory and the two weights problemJun 08 2013The famous two weights problem consists in characterising all possible pairs of weights such that the Hardy projection is bounded between the corresponding weighted $L^2$ spaces. Koosis' theorem of 1980 gives a way to construct a certain class of pairs ... More

Exponential-Uniform Identities Related to RecordsJun 05 2012We consider a rectangular grid induced by the south-west records from the planar Poisson point process in $R^2_+$. A random symmetry property of the matrix whose entries are the areas of tiles of the grid implies cute multivariate distributional identities ... More

Yet again on polynomial convergence for SDEs with a gradient-type driftJun 28 2017Jul 23 2017Bounds on convergence rate to the invariant distribution for a class of stochastic differential equations (SDEs) with a gradient-type drift are obtained.

Mild and viscosity solutions to semilinear parabolic path-dependent PDEsNov 24 2016Nov 14 2018We study and compare two concepts for weak solutions to semilinear parabolic path-dependent partial differential equations (PPDEs). The first is that of mild solutions as it appears, e.g., in the log-Laplace functionals of historical superprocesses. The ... More

Kazhdan-Laumon representations of finite Chevalley groups, character sheaves and some generalization of the Lefschetz-Verdeier trace formulaOct 01 1998In this paper we investigate the representations of reductive groups over a finite field, introduced in 1987 by D.Kazhdan and G.Laumon. We show that generically these representations are irreducible and that their character is equal to the function obtained ... More

Discrete Translates in $L^2(R)$Dec 02 2016A set $\Lambda\subset R$ is called $p$-spectral, if there is a function $\varphi\in L^p(R)$ whose $\Lambda$-translates $\{\varphi(t-\lambda),\lambda\in\Lambda\}$ span $L^p(R)$. We prove that exponentially small non-zero perturbations of the integers are ... More

$L^2-$interpolation with error and size of spectraJun 18 2008Given a compact set $S$ and a uniformly discrete sequence $\La$, we show that "approximate interpolation" of delta--functions on $\La$ by a bounded sequence of $L^2-$functions with spectra in $S$ implies an estimate on measure of $S$ through the density ... More

Homological projective duality for quadricsFeb 26 2019We show that over an algebraically closed field of characteristic not equal to 2, homological projective duality for smooth quadric hypersurfaces and for double covers of projective spaces branched over smooth quadric hypersurfaces is a combination of ... More

Categorical cones and quadratic homological projective dualityFeb 26 2019We introduce the notion of a categorical cone, which provides a categorification of the classical cone over a projective variety, and use our work on categorical joins to describe its behavior under homological projective duality. In particular, our construction ... More

Categorical joinsMar 31 2018Feb 26 2019We introduce the notion of a categorical join, which can be thought of as a categorification of the classical join of two projective varieties. This notion is in the spirit of homological projective duality, which categorifies classical projective duality. ... More

Fast gradient descent method for convex optimization problems with an oracle that generates a $(δ,L)$-model of a function in a requested pointNov 07 2017Feb 02 2019In this article we propose a new concept of a $(\delta,L)$-model of a function which generalizes the concept of the $(\delta,L)$-oracle (Devolder-Glineur-Nesterov). Using this concept we describe the gradient descent method and the fast gradient descent ... More

Moments of random sums and Robbins' problem of optimal stoppingJul 17 2011Robbins' problem of optimal stopping asks one to minimise the expected {\it rank} of observation chosen by some nonanticipating stopping rule. We settle a conjecture regarding the {\it value} of the stopped variable under the rule optimal in the sense ... More

Governing Singularities of Schubert VarietiesMar 12 2006Jun 29 2006We present a combinatorial and computational commutative algebra methodology for studying singularities of Schubert varieties of flag manifolds. We define the combinatorial notion of *interval pattern avoidance*. For "reasonable" invariants P of singularities, ... More

Scattering theory and Banach space valued singular integralsNov 28 2012We give a new sufficient condition for existence and completeness of wave operators in abstract scattering theory. This condition generalises both trace class and smooth approaches to scattering theory. Our construction is based on estimates for the Cauchy ... More

Subtle Characteristic ClassesJan 26 2014We construct new subtle Stiefel--Whitney classes of quadratic forms. These classes are much more informative than the ones introduced by Milnor. In particular, they see all the powers of the fundamental ideal of the Witt ring, contain the Arason invariant ... More

Diagonalization of the Finite Hilbert Transform on two adjacent intervalsNov 06 2015We study the interior problem of tomography. The starting point is the Gelfand-Graev formula, which converts the tomographic data into the finite Hilbert transform (FHT) of an unknown function $f$ along a collection of lines. Pick one such line, call ... More

Magnetic susceptibility of the quark condensate via holographyFeb 11 2009Jan 13 2010We discuss the holographic derivation of the magnetic susceptibility of the quark condensate. It is found that the susceptibility emerges upon the account of the Chern-Simons term in the holographic action. We demonstrate that Vainshtein's relation is ... More

On Beurling's sampling theorem in $\R^n$Jun 03 2011We present an elementary proof of the classical Beurling sampling theorem which gives a sufficient condition for sampling of multi-dimensional band-limited functions.

Regenerative compositions in the case of slow variation: A renewal theory approachSep 27 2011Sep 01 2012A regenerative composition structure is a sequence of ordered partitions derived from the range of a subordinator by a natural sampling procedure. In this paper, we extend previous studies Barbour and Gnedin (2006), Gnedin, Iksanov and Marynych (2010) ... More

Derived categories of Gushel-Mukai varietiesMay 21 2016We study the derived categories of coherent sheaves on Gushel-Mukai varieties. In the derived category of such a variety, we isolate a special semiorthogonal component, which is a K3 or Enriques category according to whether the dimension of the variety ... More

Mild and viscosity solutions to quasilinear parabolic path-dependent PDEsNov 24 2016We study and compare two different concepts for weak solutions to quasilinear parabolic path-dependent partial differential equations (PPDEs). The first concept is that of a mild solution as it appears, e.g., in the Laplace functionals of historical superprocesses. ... More

Discrete Translates in Function SpacesDec 02 2016Mar 16 2017We construct a Schwartz function $\varphi$ such that for every exponentially small perturbation of integers $\Lambda$, the set of translates $\{\varphi(t-\lambda), \lambda\in\Lambda\}$ spans the space $L^p(R)$, for every $p > 1$. This result remains true ... More

Paramagnetic tunneling state concept of the magnetic anomalies of amorphous insulatorsSep 05 2005A generalized tunneling model of insulating glasses is formulated, considering tunneling states to be paramagnetic centers of spin 1/2. The expression for magnetic field dependent contribution into the free energy is obtained. The derivation is made of ... More

Derived categories of cyclic covers and their branch divisorsNov 07 2014Dec 17 2015Given a variety $Y$ with a rectangular Lefschetz decomposition of its derived category, we consider a degree $n$ cyclic cover $X \to Y$ ramified over a divisor $Z \subset Y$. We construct semiorthogonal decompositions of $\mathrm{D^b}(X)$ and $\mathrm{D^b}(Z)$ ... More

Evaluation of the Einstein's strength of difference schemes for some chemical reaction-diffusion equationsMar 10 2018In this paper we present a difference algebraic technique for the evaluation of the Einstein's strength of a system of partial difference equations and apply this technique to the comparative analysis of difference schemes for chemical reaction-diffusion ... More

On the Duality between Sampling and InterpolationDec 04 2015We present a simple method based on the stability and duality of the properties of sampling and interpolation, which allows one to substantially simplify the proofs of some classical results.

When is a Schubert variety Gorenstein?Sep 25 2004Nov 21 2005A (normal) variety is Gorenstein if it is Cohen-Macualay and its canonical sheaf is a line bundle. This property, which measures the ``pathology'' of the singularities of a variety, is thus stronger than Cohen-Macualayness, but is also weaker than smoothness. ... More

Spherical structures on torus knots and linksAug 02 2010Jul 07 2011The present paper considers two infinite families of cone-manifolds endowed with spherical metric. The singular strata is either the torus knot ${\rm t}(2n+1, 2)$ or the torus link ${\rm t}(2n, 2)$. Domains of existence for a spherical metric are found ... More

String center of mass operator and its effect on BRST cohomologyNov 15 1995We consider the theory of bosonic closed strings on the flat background R(25,1). We show how the BRST complex can be extended to a complex where the string center of mass operator, x^mu_0, is well defined. We investigate the cohomology of the extended ... More

Homological projective duality for quadricsFeb 26 2019Mar 01 2019We show that over an algebraically closed field of characteristic not equal to 2, homological projective duality for smooth quadric hypersurfaces and for double covers of projective spaces branched over smooth quadric hypersurfaces is a combination of ... More

Categorical cones and quadratic homological projective dualityFeb 26 2019Mar 01 2019We introduce the notion of a categorical cone, which provides a categorification of the classical cone over a projective variety, and use our work on categorical joins to describe its behavior under homological projective duality. In particular, our construction ... More

An ICT-Based Real-Time Surveillance System for Controlling Dengue in Sri LankaMay 16 2014Dengue is a notifiable communicable disease in Sri Lanka since 1996. Dengue fever spread rapidly among people living in most of the districts of Sri Lanka. The present notification system of dengue communicable diseases which is enforced by law is a passive ... More

Approximation of discrete functions and size of spectrumApr 02 2013Let $\Lambda$ be a uniformly discrete set and $S$ be a compact set in $R$. We prove that if there exists a bounded sequence of functions in Paley--Wiener space $PW_S$, which approximates $\delta-$functions on $\Lambda$ with $l^2-$error $d$, then measure($S$)$\geq ... More

Full exceptional collections on the Lagrangian Grassmannians LG(4,8) and LG(5,10)Oct 13 2009We construct full exceptional collections of vector bundles on the Lagrangian Grassmannians LG(4,8) and LG(5,10).

Cauchy independent measures and super-additivity of analytic capacityNov 12 2012We show that, given a family of discs centered at a nice curve, the analytic capacities of arbitrary subsets of these discs add up. However we need that the discs in question would be slightly separated, and it is not clear whether the separation condition ... More

Random "dyadic" lattice in geometrically doubling metric space and $A_2$ conjectureMar 27 2011Apr 21 2011Recently three proofs of the $A_2$-conjecture were obtained. All of them are "glued" to euclidian space and a special choice of one random dyadic lattice. We build a random "dyadic" lattice in any doubling metric space which have properties that are enough ... More

Reachability in Higher-Order-CountersJun 05 2013Higher-order counter automata (\HOCS) can be either seen as a restriction of higher-order pushdown automata (\HOPS) to a unary stack alphabet, or as an extension of counter automata to higher levels. We distinguish two principal kinds of \HOCS: those ... More

Paramagnetic tunneling state concept of the low-temperature magnetic anomalies of multicomponent insulating glassesMar 17 2006A generalized tunneling model of multicomponent insulating glasses is formulated, considering tunneling states to be paramagnetic centers of the electronic hole type. The expression for magnetic field dependent contribution into the free energy is obtained. ... More

Exceptional collections on isotropic GrassmanniansOct 25 2011Sep 13 2015We introduce a new construction of exceptional objects in the derived category of coherent sheaves on a compact homogeneous space of a semisimple algebraic group and show that it produces exceptional collections of the length equal to the rank of the ... More

On multi-dimensional sampling and interpolationApr 02 2013The paper discusses sharp sufficient conditions for interpolation and sampling for functions of n variables with convex spectrum. When n=1, the classical theorems of Ingham and Beurling state that the critical values in the estimates from above (from ... More

Limit theorems for the number of occupied boxes in the Bernoulli sieveJan 27 2010The Bernoulli sieve is a version of the classical `balls-in-boxes' occupancy scheme, in which random frequencies of infinitely many boxes are produced by a multiplicative renewal process, also known as the residual allocation model or stick-breaking. ... More

A generalization of the Erdős-Turán law for the order of random permutationApr 26 2011May 03 2012We consider random permutations derived by sampling from stick-breaking partitions of the unit interval. The cycle structure of such a permutation can be associated with the path of a decreasing Markov chain on $n$ integers. Under certain assumptions ... More

Time-periodic Néel wall motionsJun 24 2010In thin ferromagnetic films, the predominance of the magnetic shape anisotropy leads to in-plane magnetizations. The simplest domain wall in this geometry is the one-dimensional Neel wall that connects two magnetizations of opposite sign by a planar 180 ... More

Stars and singularities: Stellar phenomena near a massive black holeFeb 12 2002This is a pedagogical review of recent results on the interactions of central massive black holes with stars very near them, focused on the black hole in the center of the Milky Way. Table of contents: [1] Introduction [2] Stellar dynamics near a black ... More

The Galactic Center as a laboratory for extreme mass ratio gravitational wave source dynamicsJul 11 2008Jul 16 2008The massive Galactic black hole and the stars around it are a unique laboratory for studying how relaxation processes lead to close interactions of stars and compact remnants with the central massive black hole, in particular those leading to the emission ... More

Analysis of energetic models for rate-independent materialsMay 01 2003We consider rate-independent models which are defined via two functionals: the time-dependent energy-storage functional $\calI:[0,T]\ti X\to [0,\infty]$ and the dissipation distance $\calD:X\ti X\to[0,\infty]$. A function $z:[0,T]\to X$ is called a solution ... More

Expander Graphs in Pure and Applied MathematicsMay 12 2011Expander graphs are highly connected sparse finite graphs. They play an important role in computer science as basic building blocks for network constructions, error correcting codes, algorithms and more. In recent years they have started to play an increasing ... More

Rayleigh-Bénard Convection as a Nambu-metriplectic problemMar 31 2008May 14 2008The traditional Hamiltonian structure of the equations governing conservative Rayleigh-B\'enard convection (RBC) is singular, i.e. it's Poisson bracket possesses nontrivial Casimir functionals. We show that a special form of one of these Casimirs can ... More

A modular analogue of Morozov's theorem on maximal subalgebras of simple Lie algebrasDec 17 2015Jan 23 2016Let $G$ be a simple algebraic group over an algebraically closed field of characteristic $p>0$ and suppose that $p$ is a very good prime for $G$. We prove that any maximal Lie subalgebra $M$ of $\mathfrak{g} = {\rm Lie}(G)$ with ${\rm rad}(M) \ne 0$ has ... More

Magnetic Behavior of the Cuprate SuperconductorsMay 17 1995I review recent work on magnetic dynamics of the high temperature superconductors using a model that combines two weakly interacting species of low-energy excitations: the antiferromagnetic spin waves which carry spin-1 and no charge, and Fermi-liquid-like ... More

Recursive Definitions of Monadic FunctionsDec 22 2010Using standard domain-theoretic fixed-points, we present an approach for defining recursive functions that are formulated in monadic style. The method works both in the simple option monad and the state-exception monad of Isabelle/HOL's imperative programming ... More

Function Weighted Metric Discovery for Unreliable FunctionsOct 31 2016Nov 02 2016We consider building a function adapted diffusion operator high dimensional data $X$ when the function $F$ can only be evaluated on large subsets of the data, and possibly only depends on a small subset of the features. Our method breaks $X$ up into hierarchical ... More

Magnetoconductivity in the presence of Bychkov-Rashba spin-orbit interactionJun 24 2006A closed-form analytic formula for the magnetoconductivity in the diffusive regime is derived in the presence of Bychkov-Rashba spin-orbit interaction in two dimensions. It is shown that at low fields B << B_{so}, where B_{so} is the characteristic field ... More

A derived category approach to Kempf's vanishing theoremNov 30 2016We give a proof of the property of the Steinberg character that implies Kempf's vanishing theorem. Our argument is based on the structure of derived categories of coherent sheaves on flag varieties.

A quantum measure of the multiverseDec 03 2013Dec 11 2013It has been recently suggested that probabilities of different events in the multiverse are given by the frequencies at which these events are encountered along the worldline of a geodesic observer (the "watcher"). Here I discuss an extension of this ... More

On cosmic natural selectionOct 04 2006Nov 27 2006The rate of black hole formation can be increased by increasing the value of the cosmological constant. This falsifies Smolin's conjecture that the values of all constants of nature are adjusted to maximize black hole production.

On the factor ordering problem in stochastic inflationFeb 01 1999The stochastic approach to inflation suffers from ambiguities due to the arbitrary choice of the time variable and due to the choice of the factor ordering in the corresponding Fokker-Planck equation. Here it is shown that both ambiguities can be removed ... More

Predictions from Quantum CosmologyJun 06 1994Oct 27 1994The world view suggested by quantum cosmology is that inflating universes with all possible values of the fundamental constants are spontaneously created out of nothing. I explore the consequences of the assumption that we are a `typical' civilization ... More

Quantum cosmology and eternal inflationApr 18 2002This contribution consists of two parts. In the first part, I review the tunneling approach to quantum cosmology and comment on the alternative approaches. In the second part, I discuss the relation between quantum cosmology and eternal inflation. In ... More

Quantum Cosmology and the Constants of NatureDec 15 1995In models where the constants of Nature can take more than one set of values, the cosmological wave function $\psi$ describes an ensemble of universes with different values of the constants. The probability distribution for the constants can be determined ... More

Predictions from Quantum CosmologyJul 07 1995Nov 20 1995After reviewing the general ideas of quantum cosmology (Wheeler-DeWitt equation, boundary conditions, interpretation of $\psi$), I discuss how these ideas can be tested observationally. Observational predictions differ for different choices of boundary ... More

Extended Deligne-Lusztig varieties for general and special linear groupsNov 24 2009Sep 30 2010We give a generalisation of Deligne-Lusztig varieties for general and special linear groups over finite quotients of the ring of integers in a non-archimedean local field. Previously, a generalisation was given by Lusztig by attaching certain varieties ... More

Representations of reductive groups over finite rings and extended Deligne-Lusztig varietiesMar 28 2004In a previous paper it was shown that a certain family of varieties suggested by Lusztig, is not enough to construct all irreducible complex representations of reductive groups over finite rings coming from the ring of integers in a local field, modulo ... More

Infinitesimal Hecke algebras of so_NJun 06 2013Aug 05 2014In this article we classify all infinitesimal Hecke algebras of so_N. We establish isomorphism of their universal versions and the W-algebras of so_{N+2m+1} with a 1-block nilpotent element of the Jordan type (1,...,1,2m+1). This should be considered ... More

QCD Sum Rules for Heavy Flavour PhysicsAug 24 2001Uses of QCD sum rules for heavy flavoured hadrons are discussed. "Standard" applications such as the determination of the $b$, $c$ quark masses, the calculation of $f_B$, $f_D$ and of the heavy-to-light form factors are overviewed. Furthermore, a new ... More