5 papers
Distance matrices, random metrics and Urysohn space
A. Vershik
We introduce an universum of the Polish (=complete separable metric) space - the convex cone of distance matrices and study its geometry. It happened that the generic Polish spaces…
Geometry and dynamics on the free solvable groups
Anatoly Vershik
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
Grigori Olshanski, Amitai Regev, Anatoly Vershik
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 conv…
Statistical properties of braid groups in locally free approximation
A. M. Vershik, S. Nechaev, R. Bikbov
Statistical and probabilistic characteristics of locally free group with growing number of generators are defined and their application to statistics of braid groups is given.
Bijective arithmetic codings of hyperbolic automorphisms of the 2-torus, and binary quadratic forms
Nikita Sidorov, Anatoly Vershik
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 en…