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Asymptotics of Plancherel measures for symmetric groups

- A. Borodin, A. Okounkov, G. Olshanski
- Mathematics
- 5 May 1999

1.1. Plancherel measures. Given a finite group G, by the corresponding Plancherel measure we mean the probability measure on the set G∧ of irreducible representations of G which assigns to a… Expand

Macdonald processes

- A. Borodin, Ivan Corwin
- Mathematics
- 18 November 2011

Macdonald processes are probability measures on sequences of partitions defined in terms of nonnegative specializations of the Macdonald symmetric functions and two Macdonald parameters $$q,t \in… Expand

Infinite Random Matrices and Ergodic Measures

- A. Borodin, G. Olshanski
- Mathematics, Computer Science
- 11 October 2000

TLDR

Anisotropic Growth of Random Surfaces in 2 + 1 Dimensions

- A. Borodin, P. Ferrari
- Mathematics
- 18 April 2008

We construct a family of stochastic growth models in 2 + 1 dimensions, that belong to the anisotropic KPZ class. Appropriate projections of these models yield 1 + 1 dimensional growth models in the… Expand

A Fredholm determinant formula for Toeplitz determinants

- A. Borodin, A. Okounkov
- Mathematics
- 25 July 1999

We prove a formula expressing a generaln byn Toeplitz determinant as a Fredholm determinant of an operator 1 −K acting onl2(n,n+1,...), where the kernelK admits an integral representation in terms of… Expand

Eynard–Mehta Theorem, Schur Process, and their Pfaffian Analogs

- A. Borodin, E. Rains
- Mathematics
- 21 September 2004

We give simple linear algebraic proofs of the Eynard–Mehta theorem, the Okounkov-Reshetikhin formula for the correlation kernel of the Schur process, and Pfaffian analogs of these results. We also… Expand

Periodic Schur process and cylindric partitions

- A. Borodin
- Mathematics
- 1 January 2006

Periodic Schur process is a generalization of the Schur process introduced in math.CO/0107056. We compute its correlation functions and their bulk scaling limits, and discuss several applications… Expand

Large time asymptotics of growth models on space-like paths I: PushASEP

- A. Borodin, Patrik L. Ferrari Caltech, Wias Berlin
- Mathematics
- 18 July 2007

We consider a new interacting particle system on the one-dimensional lattice that interpolates between TASEP and Toom's model: A particle cannot jump to the right if the neighboring site is occupied,… Expand

Fluctuation Properties of the TASEP with Periodic Initial Configuration

- A. Borodin, P. Ferrari, M. Praehofer, T. Sasamoto
- Mathematics
- 25 August 2006

Abstract
We consider the joint distributions of particle positions for the continuous time totally asymmetric simple exclusion process (TASEP). They are expressed as Fredholm determinants with a… Expand

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