arXiv subjects

Anna Gordenko

Publications and source records attributed to Anna Gordenko.

3 recordsLinked to original sources

arXiv2020

Random dynamical systems on a real line

We study random dynamical systems on the real line, considering each dynamical system together with the one generated by the inverse maps. We show that there is a duality between forward and inverse behaviour for such systems, splitting them into four classes (in terms of both dynamical and stationary measure aspects). This is analogous to the results already known for the smooth dynamics on [0,1], established in terms of the Lyapunov exponents at the endpoints; however, our arguments are purely topological, and thus our result is applicable to the general case of homeomorphisms of the real line.

math.DS↗

arXiv2020

Limit shapes of large skew Young tableaux and a modification of the TASEP process

We present a survey of points of view on the problem of the asymptotic shape of a path between two large Young diagrams, and introduce a modification of the TASEP process related to it. This representation allows to write explicitly the functional, counting the asymptotics of the number of Young tableau close to a given one, as well as to see the sine-process on the boundary shape of a large random Young diagram.

math.PR↗

arXiv2015

Self-similarity of Jankins-Neumann ziggurat

Primarily having emerged from a topological question, Jankins-Neumann ziggurat also appears in the theory of dynamical systems on the circle. It describes an answer to the following question: given the rotation numbers of two orientation-preserving circle homeomorphisms, what can be said about the rotation number of their composition? In this paper, we consider a formula, proved by Calegari and Walker, as definition of ziggurat. Using it, we establish its self-similarity. Also, we propose a short proof of equivalence between Calegary-Walker and Jankins-Neumann's descriptions of the ziggurat.

math.DS↗