T.Nagnibeda. Dynamics of sand heaps on self-similar graphs.

A.Malyutin. Boundaries of the braid group.

A.Lodkin. Phyllotaxis and related problems.

M.Gordin. How one can see mixing.

Yu.Yakubovich. Ergodicity of some measures on partitions.

A.Gorbulsky. Vershik's scaling and secondary entropies: similarity and difference.

F.Petrov. On embeddings of metric spaces into normed spaces.

E.Goryachko. The K_0 functor and characters of the group of rational rearrangements of the segment.

1. A.M.Vershik. On the mathematical activity of A.N.Livshits.

2. A.M.Vershik. The number-theoretic version of the Morse transformation.

3. M.I.Gordin. Cohomology of dynamical systems: around Livshits' theory.

Infinite-dimensional diffusions on the Kingman simplex

Deformed Calogero-Moser systems as restrictions of infinite-dimensional classical systems of the same type

Geometry and statistics of growth models

Meinardus theorem on weighted partitions: Extensions and a probabilistic proof

The number $c_n$ of weighted partitions of an integer $n$ with parameters (weights) $b_k$, $k\geq 1$, is given by the generating function relationship $$ \sum_{n=0}^{\infty}c_nz^n=\prod_{k=1}^\infty(1-z^k)^{-b_k}. $$ Meinardus (1954) established his famous asymptotic formula for $c_n$, as $n\to \infty$, under three conditions on power and Dirichlet generating functions for $b_k$. We give a probabilistic proof of Meinardus' theorem with weakened third condition and extend the resulting version of the theorem from weighted partitions to other two classic types of decomposable combinatorial structures, which are called assemblies and selections.

This is a joint work with Dudley Stark(Queen Mary College, London) and Michael Erlihson (Technion, Haifa).

Invariant integration in spaces of discrete measures and convergent series

Discretization of the algebra of differential forms on a manifold and topological quantum field theory

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