Related papers: The mixing time for simple exclusion

We define the spectral gap of a Markov chain on a finite state space as the second-smallest singular value of the generator of the chain, generalizing the usual definition of spectral gap for reversible chains. We then define the relaxation…

We study square loss in a realizable time-series framework with martingale difference noise. Our main result is a fast rate excess risk bound which shows that whenever a trajectory hypercontractivity condition holds, the risk of the…

In this paper we establish a decoupling feature of the random interlacement process I^u in Z^d, at level u, for d \geq 3. Roughly speaking, we show that observations of I^u restricted to two disjoint subsets A_1 and A_2 of Z^d are…

Given a finite graph G, a vertex of the lamplighter graph consists of a zero-one labeling of the vertices of G, and a marked vertex of G. For transitive graphs G, we show that, up to constants, the relaxation time for simple random walk in…

We establish the first polynomial upper bound for the mixing time of random edge flips on rooted quadrangulations: we show that the spectral gap of the edge flip Markov chain on quadrangulations with $n$ faces admits, up to constants, an…

In this paper, we develop some matrix Poisson's equations satisfied by the mean and variance of the mixing time in an irreducible positive-recurrent discrete-time Markov chain with infinitely-many levels, and provide a computational…

Define $(X_n)$ on $\mathbf{Z}/q\mathbf{Z}$ by $X_{n+1} = 2X_n + b_n$, where the steps $b_n$ are chosen independently at random from $-1, 0, +1$. The mixing time of this random walk is known to be at most $1.02 \log_2 q$ for almost all odd…

We prove two lower bounds for stopping times of sequential tests between general composite nulls and alternatives. The first lower bound is for the setting where the type-1 error level $\alpha$ approaches zero, and equals $\log(1/\alpha)$…

We introduce a framework for obtaining tight mixing times for Markov chains based on what we call restricted modified log-Sobolev inequalities. Modified log-Sobolev inequalities (MLSI) quantify the rate of relative entropy contraction for…

We show that for any semi-random transposition shuffle on $n$ cards, the mixing time of any given $k$ cards is at most $n\log k$, provided $k=o((n/\log n)^{1/2})$. In the case of the top-to-random transposition shuffle we show that there is…

We study the equilibrium fluctuations of a tagged particle in finite-range simple exclusion processes on Z^d with biased single particle jump rates. It is known the variance of the tagged particle at time t is diffusive, that is on order…

We prove a general theorem on cutoffs for symmetric simple exclusion processes on graphs with open boundaries, under the natural assumption that the graphs converge geometrically and spectrally to a compact metric measure space with…

We study the mixing time of the unit-rate zero-range process on the complete graph, in the regime where the number $n$ of sites tends to infinity while the density of particles per site stabilizes to some limit $\rho>0$. We prove that the…

In the cyclic-to-random shuffle, we are given n cards arranged in a circle. At step k, we exchange the k'th card along the circle with a uniformly chosen random card. The problem of determining the mixing time of the cyclic-to-random…

We prove the inequality $E[(X/\mu)^k] \le (\frac{k/\mu}{\log(k/\mu+1)})^k \le \exp(k^2/(2\mu))$ for sub-Poissonian random variables, such as Binomially or Poisson distributed random variables with mean $\mu$. The asymptotics $1+O(k^2/\mu)$…

We prove an upper bound on the total variation mixing time of a finite Markov chain in terms of the absolute spectral gap and the number of elements in the state space. Unlike results requiring reversibility or irreducibility, this bound is…

For any Markov source, there exist universal codes whose normalized codelength approaches the Shannon limit asymptotically as the number of samples goes to infinity. This paper investigates how fast the gap between the normalized codelength…

A simple lemma bounds $\mathrm{s.d.}(T)/\mathbb{E} T$ for hitting times $T$ in Markov chains with a certain strong monotonicity property. We show how this lemma may be applied to several increasing set-valued processes. Our main result…

In this paper, we propose a new Markov chain which generalizes random-to-random shuffling on permutations to random-to-random shuffling on linear extensions of a finite poset of size $n$. We conjecture that the second largest eigenvalue of…

In $\mathbb{Z}^d$ with $d\ge 5$, we consider the time constant $\rho_u$ associated to the chemical distance in random interlacements at low intensity $u \ll 1$. We prove an upper bound of order $u^{-1/2}$ and a lower bound of order…