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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.…

Probability · Mathematics 2025-11-04 Michael Howes

We consider the classic problem of scheduling jobs on unrelated machines so as to minimize the weighted sum of completion times. Recently, for a small constant $\varepsilon >0 $, Bansal et al. gave a $(3/2-\varepsilon)$-approximation…

Data Structures and Algorithms · Computer Science 2017-03-16 Christos Kalaitzis , Ola Svensson , Jakub Tarnawski

In this paper, we derive explicit sharp two-sided estimates for the Dirichlet heat kernels of a large class of symmetric (but not necessarily rotationally symmetric) L\'evy processes on half spaces for all $t>0$. These L\'evy processes may…

Probability · Mathematics 2016-02-22 Zhen-Qing Chen , Panki Kim

We consider boundary value problems for semilinear hyperbolic systems of the type $$ \partial_tu_j + a_j(x,\la)\partial_xu_j + b_j(x,\la,u) = 0, \; x\in(0,1), \;j=1,\dots,n $$ with smooth coefficient functions $a_j$ and $b_j$ such that…

Analysis of PDEs · Mathematics 2025-12-10 I. Kmit , L. Recke

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…

Probability · Mathematics 2016-04-21 Michael Damron , Naoki Kubota

The existence of a quantum butterfly effect in the form of exponential sensitivity to small perturbations has been under debate for a long time. Lately, this question gained increased interest due to the proposal to probe chaotic dynamics…

Statistical Mechanics · Physics 2019-04-10 Markus Schmitt , Dries Sels , Stefan Kehrein , Anatoli Polkovnikov

In this paper we introduce randomized pivots for the means of short and long memory linear processes. We show that, under the same conditions, these pivots converge in distribution to the same limit as that of their classical non-randomized…

Statistics Theory · Mathematics 2014-05-14 Miklos Csorgo , Masoud M Nasari , Mohamedou Ould-Haye

This article establishes the cutoff phenomenon in the Wasserstein distance for systems of nonlinear ordinary differential equations with a unique coercive stable fixed point subject to general additive Markovian noise in the limit of small…

Probability · Mathematics 2023-05-05 Gerardo Barrera , Michael A. Högele , Juan Carlos Pardo

We study graph ordering problems with a min-max objective. A classical problem of this type is cutwidth, where given a graph we want to order its vertices such that the number of edges crossing any point is minimized. We give a $…

Data Structures and Algorithms · Computer Science 2024-04-15 Nikhil Bansal , Dor Katzelnick , Roy Schwartz

This article generalizes the small noise cutoff phenomenon to the strong solutions of the stochastic heat equation and the damped stochastic wave equation over a bounded domain subject to additive and multiplicative Wiener and L\'evy noises…

Probability · Mathematics 2023-05-08 G. Barrera , M. A. Högele , J. C. Pardo

We present a simple and faster algorithm for computing fair cuts on undirected graphs, a concept introduced in recent work of Li et al. (SODA 2023). Informally, for any parameter $\epsilon>0$, a $(1+\epsilon)$-fair $(s,t)$-cut is an…

Data Structures and Algorithms · Computer Science 2024-12-02 Jason Li , Owen Li

In an $r$-uniform hypergraph on $n$ vertices a tight Hamilton cycle consists of $n$ edges such that there exists a cyclic ordering of the vertices where the edges correspond to consecutive segments of $r$ vertices. We provide a first…

Combinatorics · Mathematics 2021-07-01 Peter Allen , Christoph Koch , Olaf Parczyk , Yury Person

We present quantum algorithms for solving two problems regarding stochastic processes. The first algorithm prepares the thermal Gibbs state of a quantum system and runs in time almost linear in $\sqrt{N \beta/{\cal Z}}$ and polynomial in…

Quantum Physics · Physics 2017-01-11 Anirban Narayan Chowdhury , Rolando D. Somma

A simple third order compact finite element method is proposed for one-dimensional Sturm-Liouville boundary value problems. The key idea is based on the interpolation error estimate, which can be related to the source term. Thus, a simple…

Numerical Analysis · Mathematics 2021-08-17 Baiying Dong , Zhilin Li

We study the problem of computing the minimum cut in a weighted distributed message-passing networks (the CONGEST model). Let $\lambda$ be the minimum cut, $n$ be the number of nodes in the network, and $D$ be the network diameter. Our…

Data Structures and Algorithms · Computer Science 2014-08-05 Danupon Nanongkai , Hsin-Hao Su

We investigate the mixing time of the capacity $k$ simple exclusion process (also called the partial exclusion process) of Schultz and Sandow with $m$ particles on a segment of length $N$. We show that the $k$-SEP exhibits cutoff at time…

Probability · Mathematics 2024-01-17 Eyob Tsegaye

The paper deals with the asymptotic properties of a random jump process in a high contrast periodic medium in $\mathbb R^d$, $d\geq 1$. We show that if the coordinates of the random jump process in $\mathbb R^d$ are equipped with an extra…

Probability · Mathematics 2024-02-13 Andrey Piatnitski , Elena Zhizhina

We consider the zero-range process with arbitrary bounded monotone rates on the complete graph, in the regime where the number of sites diverges while the density of particles per site converges. We determine the asymptotics of the mixing…

Probability · Mathematics 2018-11-09 Jonathan Hermon , Justin Salez

We study algorithmic and structural aspects of connectivity in hypergraphs. Given a hypergraph $H=(V,E)$ with $n = |V|$, $m = |E|$ and $p = \sum_{e \in E} |e|$ the best known algorithm to compute a global minimum cut in $H$ runs in time…

Data Structures and Algorithms · Computer Science 2017-05-16 Chandra Chekuri , Chao Xu

I describe a subtraction scheme for the next-to-next-to-leading order calculation of single inclusive production at hadron colliders. Such processes include Drell-Yan, W^{+/-}, Z and Higgs Boson production. The key to such a calculation is…

High Energy Physics - Phenomenology · Physics 2009-11-10 William B. Kilgore
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