All entries (with papers and talks), page 5

[paper] Operators and Markov Processes on Branching Graphs

[2011/11/15]

We present a unified approach to various examples of Markov dynamics on partitions studied by Borodin, Olshanski, Fulman, and the author. Our technique generalizes the Kerov’s operators first appeared in [Okounkov, arXiv:math/0002135], and also stems from the study of duality of graded graphs in [Fomin, 1994].

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[talk] Operators and Markov Dynamics on Branching Graphs

The talk is based on [8] and describes $\mathfrak{sl}(2,\mathbb{C})$ structures behind Markov jump processes on the Young and related branching graphs

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[paper] On Measures on Partitions Arising in Harmonic Analysis for Linear and Projective Characters of the Infinite Symmetric Group

[2011/07/04]

The z-measures on partitions originated from the problem of harmonic analysis of linear representations of the infinite symmetric group in the works of Kerov, Olshanski and Vershik (1993, 2004). A similar family corresponding to projective representations was introduced by Borodin (1997). The latter measures live on strict partitions (i.e., partitions with distinct parts), and the z-measures are supported by all partitions. In this note we describe some combinatorial relations between these two families of measures using the well-known doubling of shifted Young diagrams.

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[paper] Pfaffian Stochastic Dynamics of Strict Partitions

[2010/10/15]

We study a family of continuous time Markov jump processes on strict partitions (partitions with distinct parts) preserving the distributions introduced by Borodin (1997) in connection with projective representations of the infinite symmetric group.

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[paper] Random Strict Partitions and Determinantal Point Processes

[2010/02/13]

In this note we present new examples of determinantal point processes with infinitely many particles.

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[talk] Infinite-dimensional Diffusions Related to the Two-parameter Poisson-Dirichlet Distributions

The talk describes population genetics perspective behind infinite-dimensional diffusions preserving the two-parameter Poisson–Dirichlet distributions and related models. It is based on [2].

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[talk] Infinite-Dimensional Diffusion Processes Approximated by Finite Markov Chains on Partitions

The talk describes algebraic/combinatorial perspective behind infinite-dimensional diffusions preserving the two-parameter Poisson–Dirichlet distributions and related models. It is based on [2], see also [4], [8]

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[paper] Random Walks on Strict Partitions

[2009/04/11]

We consider a certain sequence of random walks. The state space of the n-th random walk is the set of all strict partitions of n (that is, partitions without equal parts). We prove that, as n goes to infinity, these random walks converge to a continuous-time Markov process.

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A dynamics of the four most common alleles. The hitting of finite-dimensional subspaces is evident

[paper] A Two-parameter Family of Infinite-dimensional Diffusions in the Kingman Simplex

[2007/08/17]

The aim of the paper is to introduce a two-parameter family of infinite-dimensional diffusion processes $X(\alpha,\theta)$ related to Pitman’s two-parameter Poisson-Dirichlet distributions $PD(\alpha,\theta)$.

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