Related papers: The Simple Exclusion Process on the Circle has a d…
We prove a cutoff for the random walk on random $n$-lifts of finite weighted graphs, even when the random walk on the base graph $\mathcal{G}$ of the lift is not reversible. The mixing time is w.h.p. $t_{mix}=h^{-1}\log n$, where $h$ is a…
Consider a sequence of continuous-time irreducible reversible Markov chains and a sequence of initial distributions, $\mu_n$. The sequence is said to exhibit $\mu_n$-cutoff if the convergence to stationarity in total variation distance is…
This paper studies the random walk on the hypercube $(\mathbb{Z}/2\mathbb{Z})^n$ which at each step flips $k$ randomly chosen coordinates. We prove that the mixing time for this walk is of order $\frac{n}{k} \log n$. We also prove that if…
In this paper, the operation of totally asymmetric simple exclusion process with one or two shortcuts under open boundary conditions is discussed. Using both mathematical analysis and numerical simulations, we have found that, according to…
We show that for any attractive Glauber-Exclusion process on the one-dimensional lattice of size $N$ with periodic boundary condition, if the corresponding hydrodynamic limit equation has a reaction term with a strictly convex potential,…
In classical probability theory, the term "cutoff" describes the property of some Markov chains to jump from (close to) their initial configuration to (close to) completely mixed in a very narrow window of time. We investigate how coherent…
We consider Glauber dynamics for the Ising model on the complete graph on $n$ vertices, known as the Curie-Weiss model. It is well-known that the mixing-time in the high temperature regime ($\beta < 1$) has order $n\log n$, whereas the…
Exclusion processes became paradigmatic models of nonequilibrium interacting particle systems of wide range applicability both across the natural and the applied, social and technological sciences. Usually they are defined as a…
We study the asymptotics of a Markovian system of $N \geq 3$ particles in $[0,1]^d$ in which, at each step in discrete time, the particle farthest from the current centre of mass is removed and replaced by an independent $U [0,1]^d$ random…
We consider a one-dimensional nearest-neighbor interacting particle system, which is a mixture of the simple exclusion process and the voter model. The state space is taken to be the countable set of the configurations that have a finite…
We prove that the mixing time of driven-dissipative activated random walk on an interval of length $n$ with uniform or central driving exhibits cutoff at $n$ times the critical density for activated random walk on the integers. The proof…
The edge flipping is a non-reversible Markov chain on a given connected graph, which is defined by Chung and Graham in [CG12]. In the same paper, its eigenvalues and stationary distributions for some classes of graphs are identified. We…
We prove an upper bound for the $\varepsilon$-mixing time of the symmetric exclusion process on any graph G, with any feasible number of particles. Our estimate is proportional to $\mathsf{T}_{\mathsf{RW}(G)}\ln(|V|/\varepsilon)$, where |V|…
We give a short proof that low-temperature dynamics for the Sherrington-Kirkpatrick model have mixing time exponential in the system size, based on the recently proved existence of gapped spin configurations by (Minzer-Sah-Sawhney 2023,…
The time needed for a particle to exit a confining domain through a small window, called the narrow escape time (NET), is a limiting factor of various processes, such as some biochemical reactions in cells. Obtaining an estimate of the mean…
The edge flipping is a non-reversible Markov chain on a given connected graph, which is defined by Chung and Graham. In the same paper, its eigenvalues and stationary distributions for some classes of graphs are identified. We further study…
We investigate a quadratic dynamical system known as nonlinear recombinations. This system models the evolution of a probability measure over the Boolean cube, converging to the stationary state obtained as the product of the initial…
We use the correlation matrix of the generating distribution to determine the mixing time for random walks on the torus $(\mathbb{Z}/q\mathbb{Z})^n$. We present our method in the context of the Diaconis-Gangolli random walk on both the $1…
The Fredrickson-Andersen one spin facilitated model belongs to the class of Kinetically Constrained Spin Models. It is a non attractive process with positive spectral gap. In this paper we give a precise result on the relaxation for this…
We consider completely irrational nilflows on any nilmanifold of step at least $2$. We show that there exists a dense set of smooth time-changes such that any time-change in this class which is not measurably trivial gives rise to a mixing…