Vadim Malyshev

Lyapounov Functions for Jackson Networks

We construct explicitly Lyapounov functions for Markovian Jackson networks. Two direct corollaries are obtained: first a proof of the necessary and sufficient conditions for ergodicity, without using the famous Jacksons product form; secondly, an exponential convergence rate to the stationary distribution. We also consider small perturbations of the transition probabilities yielding thus non-Jackson networks and prove that the corresponding stationary distribution is an analytic function of these perturbations.

Phase transitions in the time synchronization model

There are two types

Critical states of strongly interacting many-particle systems on a circle

i=1,2

Phase transitions in the one-dimensional coulomb medium

of particles on the line

Linear Hamiltonian Systems under Microscopic Random Influence

{\bf R}

Accumulation on the boundary for a one-dimensional stochastic particle system

, with

Fine structure of a one-dimensional discrete point system

N_{i}

Homeostasis in Chemical Reaction Pathways

particles of type

The Genus 0 Case

i\,

A Two-Coupled Processor Model

. Each particle of type i moves with constant velocity