Supported by the Austrian Federal Ministry of Education, Science and Culture (2009)
The Erwin, Schrödinger International Boltzmanngasse, Klaus Schmidt, Anatoly Vershik, Klaus Schmidt, Anatoly Vershik
Dedicated to the memory of our colleague and friend William Parry Abstract. In this paper we consider a special class of polymorphisms with invariant measure, the algebraic polymorphisms of compact...
Michael Ben-Or, Greg Kuperberg, and Boris Tsirelson for helpful discussions, and to (2008)
Gil Kalai, Daniel Gottesman, Pierfrancesco La Mura, Nati Linial, Simon Litsyn, Yuval Peres, ...
We will try to explore, primarily from the complexity-theoretic point of view, limitations of error-correction and fault-tolerant quan-tum computation. We consider stochastic models of quantum...
We construct explicitly and study the isometry between the spaces of square integrable functionals of an arbitrary Levy process and a vector-valued Gaussian white noise. In particular, we obtain...
Amir Dembo, Anatoly Vershik, St. Petersburg Branch, Ofer Zeitouni
Abstract We consider deviations from limit shape induced by uniformly distributed partitions (and strict partitions) of an integer n on the associated Young diagrams. We prove a full large deviation...
L.V.Kantorovich and Linear Programming (2007)
I want to write about what I know and remember about the activities of Leonid Vital'evich Kantorovich, an outstanding scientist of the 20th century; about his dramatic struggle for recognition of his...
Algebraic Polymorphisms (2007)
Schmidt, Klaus, Vershik, Anatoly
In this paper we consider a special class of polymorphisms with invariant measure, - (cf.[1])- the algebraic polymorphisms of compact groups. A general polymorphism is -- by definition -- a...
Does there exist the Lebesgue measure in the infinite-dimensional space? (2007)
We study the sigma-finite measures in the space of vector-valued distributions on the manifold $X$ with Laplace transform $$\Psi(f)=\exp\{-\theta\int_X\ln||f(x)||dx\}, \theta>0.$$ We also consider...
Twisted Burnside theorem for type II_1 groups: an example (2006)
Fel'shtyn, Alexander, Troitsky, Evgenij, Vershik, Anatoly
The purpose of the present paper is to discuss the following conjecture of Fel'shtyn and Hill, which is a generalization of the classical Burnside theorem: Let G be a countable discrete group, f its...
Thoughts on noise and quantum computing (2005)
Gil Kalai, Gil Kalai, Daniel Gottesman, Pierfrancesco La Mura, Nati Linial, Simon Litsyn, ...
We will try to explore, primarily from the complexity-theoretic point of view, limitations of error-correction and fault-tolerant quan-tum computation. We consider stochastic models of quantum...
Michael Ben-Or, Greg Kuperberg, and Boris Tsirelson for helpful discussions, and to (2005)
Gil Kalai, Daniel Gottesman, Pierfrancesco La Mura, Nati Linial, Simon Litsyn, Yuval Peres, ...
We will try to explore, primarily from the complexity-theoretic point of view, limitations of error-correction and fault-tolerant quan-tum computation. We consider stochastic models of quantum...
Harmonic analysis on the infinite symmetric group (2003)
Kerov, Sergei, Olshanski, Grigori, Vershik, Anatoly
Let S be the group of finite permutations of the naturals 1,2,... The subject of the paper is harmonic analysis for the Gelfand pair (G,K), where G stands for the product of two copies of S while K...
Fock factorizations, and decompositions of the $L^2$ spaces over general Levy processes (2003)
Vershik, Anatoly, Tsilevich, Natalia
We explicitly construct and study an isometry between the spaces of square integrable functionals of an arbitrary Levy process and a vector-valued Gaussian white noise. In particular, we obtain...
Frobenius-Schur functions (2001)
Olshanski, Grigori, Regev, Amitai, Vershik, Anatoly
The present paper is a detailed version of math/0003031. We introduce and study a new basis in the algebra of symmetric functions. The elements of this basis are called the Frobenius-Schur functions...
Geometry and dynamics on the free solvable groups (2000)
The new model for the free solvable groups of level two is given; this helps to calculate the Poisson-Furstenberg boundary of the group.
Frobenius-Schur functions: summary of results (2000)
Olshanski, Grigori, Regev, Amitai, Vershik, Anatoly
We introduce and study a family of inhomogeneous symmetric functions which we call the Frobenius-Schur functions. These functions are indexed by partitions and differ from the conventional Schur...
Frobenius-Schur Functions (1999)
Grigori Olshanski, Amitai Regev, Anatoly Vershik
We introduce and study a new basis in the algebra of symmetric functions.
Sidorov, Nikita, Vershik, Anatoly
We study the arithmetic codings of hyperbolic automorphisms of the 2-torus, i.e. the continuous mappings acting from a certain symbolic space of sequences with a finite alphabet endowed with an...
Nikita Sidorov And, Nikita Sidorov, Anatoly Vershik
We study arithmetic codings of hyperbolic automorphisms of the 2-torus, i.e. mappings acting from the symbolic space of sequences with a finite alphabet endowed with an appropriate structure of...
Large Deviations for Integer Partitions (1998)
Amir Dembo, Anatoly Vershik, St. Petersburg Branch, Ofer Zeitouni
We consider deviations from limit shape induced by uniformly distributed partitions (and strict partitions) of an integer n on the associated Young diagrams. We prove a full large deviation...
Large Deviations for Integer Partitions (1998)
Amir Dembo, Anatoly Vershik, St. Petersburg Branch, Ofer Zeitouni
We consider deviations from limit shape induced by uniformly distributed partitions (and strict partitions) of an integer n on the associated Young diagrams. We prove a full large deviation...
Arithmetic Construction of Sofic Partitions of Hyperbolic Toral Automorphisms (1998)
Richard Kenyon, Anatoly Vershik
For each irreducible hyperbolic automorphism A of the n-torus we construct a sofic system (\Sigma; oe) and an isomorphism of (\Sigma; oe) with a finite cover of (T n ; A). This construction is...
Asymptotics of Young diagrams and hook numbers (1997)
Amitai Regev, Anatoly Vershik, Givat Ram
Abstract: Asymptotic calculations are applied to study the degrees of certain sequences of characters of symmetric groups. Starting with a given partition µ, we deduce several skew diagrams which...
Asymptotics of Young diagrams and hook numbers (1997)
Amitai Regev, Anatoly Vershik, Givat Ram
Abstract: Asymptotic calculations are applied to study the degrees of certain sequences of characters of symmetric groups. Starting with a given partition, we deduce several skew diagrams which are...
Asymptotics of Young Diagrams and Hook Numbers (1997)
Amitai Regev, Anatoly Vershik, Givat Ram
: Asymptotic calculations are applied to study the degrees of certain sequences of characters of symmetric groups. Starting with a given partition ¯, we deduce several skew diagrams which are...
Ergodic properties of Erd\"os measure, the entropy of the goldenshift, and related problems (1996)
Sidorov, Nikita, Vershik, Anatoly
We define a two-sided analog of Erd\"os measure on the space of two-sided expansions with respect to the powers of the golden ratio, or, equivalently, the Erd\"os measure on the 2-torus. We construct...
THEORY OF SYMMETRIC GROUPS (1996)
The Erwin, Schrödinger International Boltzmanngasse, Andrei Okounkov, Anatoly Vershik, Andrei Okounkov, Anatoly Vershik
for Mathematical Physics,