arXiv subjects

S. A. Muzychka

Publications and source records attributed to S. A. Muzychka.

2 recordsLinked to original sources

arXiv2013

Dynamical phase transition in the simplest molecular chain model

We consider the dynamics of the simplest chain of large number $N$ of particles. We find, in the double scaling limit, the partition of the parameter space onto two domains, where for one domain the supremum (over all time interval $(0,\infty)$ of relative extension tenda to $1$ as $N\to\infty$. and for the other this supremum tends to infinity as $N\to\infty$.

math-ph↗

arXiv2011

A class of nonlinear random walks related to the Ornstein-Uhlenbeck process

Contrary to the theory of Markov processes, no general theory exists for the so called nonlinear Markov processes. We study an example of "nonlinear Markov process" related to classical probability theory, merely to random walks. This model provides interesting phenomena (absent in classical Markov chains): continuum of stationary measures, conserved quantities, convergence to stationary classical random walks etc.

math-ph↗