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Evita Nestoridi

Publications and source records attributed to Evita Nestoridi.

At least 19 recordsLinked to original sources
arXiv2026

Hitting-time mixing for the star transposition shuffle

We prove a hitting-time analogue of cutoff for the star transposition shuffle on the symmetric group S_n. Let tau be the first time at which every non-top card has been selected. We show that the shuffle is asymptotically mixed at time tau: more precisely, the total variation distance between the law of Y_tau and the uniform distribution on S_n is at most exp(-(log n)^(1/2+o(1))). Our proof compares the star transposition shuffle with the random transposition shuffle using simultaneous diagonalization of the two transition kernels, and then adapts the hitting-time strategy of Jain and Sawhney. This introduces a technique that can be applied to card shuffles that are not necessarily conjugacy invariant.

math.PR↗
arXiv2026

Mixing times of one-sided $k$-transposition shuffles

We study mixing times of the one-sided $k$-transposition shuffle. We prove that this shuffle mixes relatively slowly, even for $k$ big. Using the recent ``lifting eigenvectors'' technique of Dieker and Saliola and applying the $\ell^2$ bound, we prove different mixing behaviors and explore the occurrence of cutoff depending on $k$.

math.PR↗
arXiv2026

Shuffling via sums of Jucys--Murphy Elements

We consider a family of card shuffles of $n$ cards in which the allowed moves involve transpositions corresponding to the Jucys--Murphy elements of the symmetric group $\{S_m\}_{m \leq n}$. We determine the eigenvalues of the corresponding $n! \times n!$ transition matrices of these shuffles and study the mixing times for a special case, the $k$--star transpositions shuffle, a natural interpolation between the random transpositions shuffle, introduced and studied by Diaconis and Shahshahani, and the star transpositions shuffle, introduced and studied by Diaconis. We prove that the $k$--star transpositions shuffle exhibits total variation cutoff at $\frac{2n-(k+1)}{2(n-1)}n\log n$ with a window of $\frac{2n-(k+1)}{2(n-1)}n$. Furthermore, in the regimes $k/n \rightarrow 0$ or $k/n \rightarrow 1$, this shuffle has the same limit profile as random transpositions, which has been fully determined by Teyssier.

math.CO↗
arXiv2026

Limit Profiles for Separation Distance

This paper studies limit profiles for the separation distance. A limit profile records the limiting shape of the distance to stationarity inside the cutoff window, at times of the form $t_n+cw_n$. We start with two famous card shuffles, a general setup for inverse riffle shuffles and random transpositions, and we determine their separation distance limit profiles. We then develop a spectral comparison technique and study continuity properties in the style of [Nes24; Nes25], adapted to separation distance. The comparison method is illustrated through random transpositions, as well as random walks on product groups and the hypercube.

math.PR↗
arXiv2025

Limit Profiles for Reversible Markov Chains

In a recent breakthrough, Teyssier [Tey20] introduced a new method for approximating the distance from equilibrium of a random walk on a group. He used it to study the limit profile for the random transpositions card shuffle. His techniques were restricted to conjugacy-invariant random walks on groups; we derive similar approximation lemmas for random walks on homogeneous spaces and for general reversible Markov chains. We illustrate applications of these lemmas to some famous problems: the $k$-cycle shuffle, improving results of Hough [Hou16] and Berestycki, Schramm and Zeitouni [BSZ11]; the Ehrenfest urn diffusion with many urns, improving results of Ceccherini-Silberstein, Scarabotti and Tolli [CST07]; a Gibbs sampler, which is a fundamental tool in statistical physics, with Binomial prior and hypergeometric posterior, improving results of Diaconis, Khare and Saloff-Coste [DKS08].

math.PR↗
arXiv2025

Continuity for Limit Profiles of Reversible Markov Chains

We prove that the limit profile of a sequence of reversible Markov chains exhibiting total variation cutoff is a continuous function, under a computable condition involving the spectrum of the transition matrix and the cutoff window.

math.PR↗
arXiv2025

The random walk on upper triangular matrices over $\mathbb{Z}/m \mathbb{Z}$

We study a natural random walk on the $n \times n$ upper triangular matrices, with entries in $\mathbb{Z}/m \mathbb{Z}$, generated by steps which add or subtract a uniformly random row to the row above. We show that the mixing time of this random walk is $O(m^2n \log n+ n^2 m^{o(1)})$. This answers a question of Stong and of Arias-Castro, Diaconis, and Stanley.

math.PR↗
arXiv2024

Limit Profile for Projections of Random Walks on Groups

Establishing cutoff, an abrupt transition from "not mixed" to "well mixed", is a classical topic in the theory of mixing times for Markov chains. Interest has grown recently in determining not only the existence of cutoff and the order of its mixing time and window, but the exact shape, or profile, of the convergence inside the window. Classical techniques, such as coupling or $\ell_2$-bounds, are typically too crude to establish this and there has been a push to develop general techniques. We build upon this work, extending from conjugacy-invariant random walks on groups to certain projections. We exemplify our method by analysing the $k$-particle interchange process on the complete $n$-graph with $k \asymp n$. This is a projection of the random-transposition card shuffle, which corresponds to $k = n$, analysed by Teyssier.

math.PR↗
arXiv2024

Approximating the stationary distribution of the ASEP with open boundaries

We investigate the stationary distribution of asymmetric and weakly asymmetric simple exclusion processes with open boundaries. We project the stationary distribution onto a subinterval, whose size is allowed to grow with the length of the underlying segment. Depending on the boundary parameters of the exclusion process, we provide conditions such that the stationary distribution projected onto a subinterval is close in total variation distance to a product measure.

math.PR↗
arXiv2024

Cutoff for the Biased Random Transposition Shuffle

In this paper, we study the biased random transposition shuffle, a natural generalization of the classical random transposition shuffle studied by Diaconis and Shahshahani. We diagonalize the transition matrix of the shuffle and use these eigenvalues to prove that the shuffle exhibits total variation cutoff at time $t_N = \frac{1}{2b} N \log N$ with window $N$. We also prove that the limiting distribution of the number of fixed cards near the cutoff time is Poisson.

math.PR↗
arXiv2023

Rowmotion Markov Chains

Rowmotion is a certain well-studied bijective operator on the distributive lattice $J(P)$ of order ideals of a finite poset $P$. We introduce the rowmotion Markov chain ${\bf M}_{J(P)}$ by assigning a probability $p_x$ to each $x\in P$ and using these probabilities to insert randomness into the original definition of rowmotion. More generally, we introduce a very broad family of toggle Markov chains inspired by Striker's notion of generalized toggling. We characterize when toggle Markov chains are irreducible, and we show that each toggle Markov chain has a remarkably simple stationary distribution. We also provide a second generalization of rowmotion Markov chains to the context of semidistrim lattices. Given a semidistrim lattice $L$, we assign a probability $p_j$ to each join-irreducible element $j$ of $L$ and use these probabilities to construct a rowmotion Markov chain ${\bf M}_L$. Under the assumption that each probability $p_j$ is strictly between $0$ and $1$, we prove that ${\bf M}_{L}$ is irreducible. We also compute the stationary distribution of the rowmotion Markov chain of a lattice obtained by adding a minimal element and a maximal element to a disjoint union of two chains. We bound the mixing time of ${\bf M}_{L}$ for an arbitrary semidistrim lattice $L$. In the special case when $L$ is a Boolean lattice, we use spectral methods to obtain much stronger estimates on the mixing time, showing that rowmotion Markov chains of Boolean lattices exhibit the cutoff phenomenon.

math.CO↗
arXiv2023

The $S_k$ shuffle block dynamics

We introduce and analyze the $S_k$ shuffle on $N$ cards, a natural generalization of the celebrated random adjacent transposition shuffle. In the $S_k$ shuffle, we choose uniformly at random a block of $k$ consecutive cards, and shuffle these cards according to a permutation chosen uniformly at random from the symmetric group on $k$ elements. We study the total-variation mixing time of the $S_k$ shuffle when the number of cards $N$ goes to infinity, allowing also $k=k(N)$ to grow with $N$. In particular, we show that the cutoff phenomenon occurs when $k=o(N^{\frac{1}{6}})$.

math.PR↗
arXiv2022

Mixing times for the simple exclusion process with open boundaries

We study mixing times of the symmetric and asymmetric simple exclusion process on the segment where particles are allowed to enter and exit at the endpoints. We consider different regimes depending on the entering and exiting rates as well as on the rates in the bulk, and show that the process exhibits pre-cutoff and in some cases cutoff. Our main contribution is to study mixing times for the asymmetric simple exclusion process with open boundaries. We show that the order of the mixing time can be linear or exponential in the size of the segment depending on the choice of the boundary parameters, proving a strikingly different (and richer) behavior for the simple exclusion process with open boundaries than for the process on the closed segment. Our arguments combine coupling, second class particle and censoring techniques with current estimates. A novel idea is the use of multi-species particle arguments, where the particles only obey a partial ordering.

math.PR↗
arXiv2022

The Limit Profile of Star Transpositions

We prove that the limit profile of star transpositions at time $t= n \log n +cn$ is equal to $d_{\text{T.V.}}(\text{Poiss}(1+e^{-c}), \text{Poiss}(1))$. We prove this by developing a technique for comparing the limit profile behavior of two reversible Markov chains on the same space, that share the same stationary distribution and eigenbasis. We then compare the limit profile of star transpositions to the limit profile of random transpositions, as studied in \cite{Teyssier}, and prove that they have the same limit profile at the respective cutoff times.

math.PR↗
arXiv2021

Cutoff on trees is rare

We study the simple random walk on trees and give estimates on the mixing and relaxation time. Relying on a recent characterization by Basu, Hermon and Peres, we give geometric criteria, which are easy to verify and allow to determine whether the cutoff phenomenon occurs. We thoroughly discuss families of trees with cutoff, and show how our criteria can be used to prove the absence of cutoff for several classes of trees, including spherically symmetric trees, Galton-Watson trees of a fixed height, and sequences of random trees converging to the Brownian CRT.

math.PR↗
arXiv2020

Cutoff for the Bernoulli-Laplace urn model with $o(n)$ swaps

We study the mixing time of the $(n,k)$ Bernoulli--Laplace urn model, where $k\in\{0,1,\ldots,n\}$. Consider two urns, each containing $n$ balls, so that when combined they have precisely $n$ red balls and $n$ white balls. At each step of the process choose uniformly at random $k$ balls from the left urn and $k$ balls from the right urn and switch them simultaneously. We show that if $k=o(n)$, this Markov chain exhibits mixing time cutoff at $\frac{n}{4k}\log n$ and window of the order $\frac{n}{k}\log\log n$. This is an extension of a classical theorem of Diaconis and Shahshahani who treated the case $k=1$.

math.PR↗
arXiv2019

On the spectrum of random walks on complete finite $d$-ary trees

In the present paper, we determine the full spectrum of the simple random walk on finite, complete $d$-ary trees. We also find an eigenbasis for the transition matrix. As an application, we apply our results to get a lower bound for the interchange process on complete, finite d-ary trees, which we conjecture to be sharp.

math.PR↗