相关论文: Cutoff for congestion dynamics and related general…
We derive upper and lower bounds on the convergence behavior of certain classes of one-parameter quantum dynamical semigroups. The classes we consider consist of tensor product channels and of channels with commuting Liouvillians. We…
We study convergence to equilibrium for a large class of Markov chains in random environment. The chains are sparse in the sense that in every row of the transition matrix $P$ the mass is essentially concentrated on few entries. Moreover,…
We study the speed of convergence of the Swendsen-Wang (SW) dynamics for the $q$-state ferromagnetic Potts model on the $n$-vertex complete graph, known as the mean-field model. The SW dynamics was introduced as an attractive alternative to…
Discovered in the context of card shuffling by Aldous, Diaconis and Shahshahani, the cutoff phenomenon has since then been established in a variety of Markov chains. However, proving cutoff remains a delicate affair, which requires a…
The cutoff phenomenon describes a sharp transition in the convergence of a Markov chain to equilibrium. In recent work, the authors established cutoff and its location for the stochastic Ising model on the $d$-dimensional torus $(Z/nZ)^d$…
The cutoff phenomenon describes a sharp transition in the convergence of a family of ergodic finite Markov chains to equilibrium. Many natural families of chains are believed to exhibit cutoff, and yet establishing this fact is often…
The cutoff phenomena for Markovian dynamics have been observed and rigorously verified for a multitude of models, particularly for Glauber-type dynamics on spin systems. However, prior studies have barely considered irreversible chains. In…
For each $n,r \geq 0$, let $KG(n,r)$ denote the Kneser Graph; that whose vertices are labeled by $r$-element subsets of $n$, and whose edges indicate that the corresponding subsets are disjoint. Fixing $r$ and allowing $n$ to vary, one…
We consider a variant of the configuration model with an embedded community structure and study the mixing properties of a simple random walk on it. Every vertex has an internal $\mathrm{deg}^{\text{int}}\geq 3$ and an outgoing…
We analyze a Markov chain, known as the product replacement chain, on the set of generating $n$-tuples of a fixed finite group $G$. We show that as $n \rightarrow \infty$, the total-variation mixing time of the chain has a cutoff at time…
We investigate the mixing properties of a finite Markov chain in random environment defined as a mixture of a deterministic chain and a chain whose state space has been permuted uniformly at random. This work is the counterpart of a…
A finite ergodic Markov chain is said to exhibit cutoff if its distance to stationarity remains close to 1 over a certain number of iterations and then abruptly drops to near 0 on a much shorter time scale. Discovered in the context of card…
We consider the reversible exclusion process with reservoirs on arbitrary networks. We characterize the spectral gap, mixing time, and mixing window of the process, in terms of certain simple statistics of the underlying network. Among…
We investigate the mixing properties of a model of reversible Markov chains in random environment, which notably contains the simple random walk on the superposition of a deterministic graph and a second graph whose vertex set has been…
We analyze the convergence rates for a family of auto-regressive Markov chains $(X^{(n)}_k)_{k\geq 0}$ on $\mathbb R^d$, where at each step a randomly chosen coordinate is replaced by a noisy damped weighted average of the others. The…
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…
We study the cut-off phenomenon for a family of stochastic small perturbations of a one dimensional dynamical system. We will focus in a semi-flow of a deterministic differential equation which is perturbed by adding to the dynamics a white…
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…
We investigate congestion-aware control of quantum repeater nodes operating under stochastic traffic and finite memory coherence. Entanglement generation is modeled as a probabilistic process producing Werner states subject to depolarizing…
Families of symmetric simple random walks on Cayley graphs of Abelian groups with a bound on the number of generators are shown to never have sharp cut off in the sense of [1], [3], or [5]. Here convergence to the stationary distribution is…