Related papers: The Limit Profile of Star Transpositions

Equivalence of the spectral gap, exponential integrability of hitting times and Lyapunov conditions are well known. We give here the correspondance (with quantitative results) for reversible diffusion processes. As a consequence, we…

We give an upper bound on the total variation distance between the linear eigenvalue statistic, properly scaled and centred, of a random matrix with a variance profile and the standard Gaussian random variable. The second order Poincar\'e…

This paper explores the mixing time of the random transposition walk on permutations with one-sided interval restrictions. In particular, we're interested in the notion of cutoff, a phenomenon which occurs when mixing occurs in a window of…

Let M be a noncompact metric space in which every closed ball is compact, and let G be a semigroup of Lipschitz mappings of M. Denote by (Y_n)_{n\geq1} a sequence of independent G-valued, identically distributed random variables (r.v.'s),…

We consider random networks whose dynamics is described by a rate equation, with transition rates $w_{nm}$ that form a symmetric matrix. The long time evolution of the system is characterized by a diffusion coefficient $D$. In one dimension…

In this paper we study the mixing time of a biased transpositions shuffle on a set of $N$ cards with $N/2$ cards of two types. For a parameter $0<a \le 1$, one type of card is chosen to transpose with a bias of $\frac{a}{N}$ and the other…

We study the limit behaviour of upper and lower bounds on expected time averages in imprecise Markov chains; a generalised type of Markov chain where the local dynamics, traditionally characterised by transition probabilities, are now…

We obtain moment and Gaussian bounds for general Lipschitz functions evaluated along the sample path of a Markov chain. We treat Markov chains on general (possibly unbounded) state spaces via a coupling method. If the first moment of the…

By a profound result of Heinrich, Novak, Wasilkowski, and Wo{\'z}niakowski the inverse of the star-discrepancy $n^*(s,\ve)$ satisfies the upper bound $n^*(s,\ve) \leq c_{\mathrm{abs}} s \ve^{-2}$. This is equivalent to the fact that for any…

Evolutionary synthesis models are a fundamental tool to interpret the properties of observed stellar systems. In order to achieve a meaningful comparison between models and real data, it is necessary to calibrate the models themselves, i.e.…

Given a sequence of polynomials $(P_n)_{n \in \mathbb{N}}$ with only nonpositive zeros, the aim of this article is to present a user-friendly approach for determining the limiting zero distribution of $P_n$ as $\mathrm{deg}\, P_n \to…

We consider first-passage percolation on the two-dimensional triangular lattice $\mathcal{T}$. Each site $v\in\mathcal{T}$ is assigned independently a passage time of either $0$ or $1$ with probability $1/2$. Denote by $B^+(0,n)$ the upper…

This article gives sharp estimates for the mixing time of the Burnside process for Sylow $p$-double cosets in the symmetric group $S_n$. This process is a Markov chain on $S_n$ which can be used to uniformly sample Sylow $p$-double cosets.…

A random hopping on a fractal network with dimension slightly above one, $d = 1 + \epsilon$, is considered as a model of transport for conducting polymers with nonmetallic conductivity. Within the real space renormalization group method of…

Consider the switch chain on the set of $d$-regular bipartite graphs on $n$ vertices with $3\leq d\leq n^{c}$, for a small universal constant $c>0$. We prove that the chain satisfies a Poincar\'e inequality with a constant of order $O(nd)$;…

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 show the convergence of the characteristic polynomial for random permutation matrices sampled from the generalized Ewens distribution. Under this distribution, the measure of a given permutation depends only on its cycle structure,…

This paper does three things: It proves a central limit theorem for novel permutation statistics (for example, the number of descents plus the number of descents in the inverse). It provides a clear illustration of a new approach to proving…

Let $Y=(y_1,y_2,...)$, $y_1\ge y_2\ge...$, be the list of sizes of the cycles in the composition of $c n$ transpositions on the set $\{1,2,...,n\}$. We prove that if $c>1/2$ is constant and $n\to\infty$, the distribution of $f(c)Y/n$…

We consider first-passage percolation on the $d$ dimensional cubic lattice for $d \geq 2$; that is, we assign independently to each edge $e$ a nonnegative random weight $t_e$ with a common distribution and consider the induced random graph…