arXiv subjects

N. Cancrini

Publications and source records attributed to N. Cancrini.

3 recordsLinked to original sources

arXiv2021

Quantitative ergodicity for the symmetric exclusion process with stationary initial data

We consider the symmetric exclusion process on the $d$-dimensional lattice with translational invariant and ergodic initial data. It is then known that as $t$ diverges the distribution of the process at time $t$ converges to a Bernoulli product measure. Assuming a summable decay of correlations of the initial data, we prove a quantitative version of this convergence by obtaining an explicit bound on the Ornstein $\bar d$-distance. The proof is based on the analysis of a two species exclusion process with annihilation.

math.PR↗

arXiv2011

On the dynamical behavior of the ABC model

We consider the ABC dynamics, with equal density of the three species, on the discrete ring with $N$ sites. In this case, the process is reversible with respect to a Gibbs measure with a mean field interaction that undergoes a second order phase transition. We analyze the relaxation time of the dynamics and show that at high temperature it grows at most as $N^2$ while it grows at least as $N^3$ at low temperature.

math.PR↗

arXiv2006

Relaxation time of $L$-reversal chains and other chromosome shuffles

We prove tight bounds on the relaxation time of the so-called $L$-reversal chain, which was introduced by R. Durrett as a stochastic model for the evolution of chromosome chains. The process is described as follows. We have $n$ distinct letters on the vertices of the ${n}$-cycle (${\mathbb{Z}}$ mod $n$); at each step, a connected subset of the graph is chosen uniformly at random among all those of length at most $L$, and the current permutation is shuffled by reversing the order of the letters over that subset. We show that the relaxation time $τ(n,L)$, defined as the inverse of the spectral gap of the associated Markov generator, satisfies $τ(n,L)=O(n\vee \frac{n^3}{L^3})$. Our results can be interpreted as strong evidence for a conjecture of R. Durrett predicting a similar behavior for the mixing time of the chain.

math.PR↗