-
作者：Hermon, Jonathan; Salez, Justin
作者单位：University of British Columbia; Universite PSL; Universite Paris-Dauphine; Universite PSL
摘要：We resolve a long-standing conjecture of Wilson (Ann. Appl. Probab. 14 (2004) 274-325), reiterated by Oliveira (2016), asserting that the mixing time of the interchange process with unit edge rates on the n-dimensional hyper-cube is of order n. This follows from a sharp inequality established at the level of Dirichlet forms, from which we also deduce that macroscopic cycles emerge in constant time, and that the log-Sobolev constant of the exclusion process is of order 1. Beyond the hypercube, ...
-
作者：Dianetti, Jodi; Ferrari, Giorgio; Fischer, Markus; Nendel, Max
作者单位：University of Bielefeld; University of Padua
摘要：We study mean field games with scalar Ito-type dynamics and costs that are submodular with respect to a suitable order relation on the state and measure space. The submodularity assumption has a number of interesting consequences. First, it allows us to prove existence of solutions via an application of Tarski's fixed point theorem, covering cases with discontinuous dependence on the measure variable. Second, it ensures that the set of solutions enjoys a lattice structure: in particular, there...
-
作者：Ernst, Philip A.; Franceschi, Sandro
作者单位：Rice University; Universite Paris Saclay
摘要：Let pi be the occupancy density of an obliquely reflected Brownian motion in the half plane and let (rho, alpha) be the polar coordinates of a point in the upper half plane. This work determines the exact asymptotic behavior of pi(rho, alpha) as rho -> infinity with alpha epsilon (0, pi). We find explicit functions a, b, c such that pi(rho, alpha) similar to(rho -> infinity) a(alpha) rho(b(alpha)) e(-c(alpha)rho). This closes an open problem first stated by Professor J. Michael Harrison in Aug...
-
作者：Foutel-Rodier, Felix; Lambert, Amaury; Schertzer, Emmanuel
作者单位：Universite Paris Cite; Sorbonne Universite; Universite PSL; College de France; Institut National de la Sante et de la Recherche Medicale (Inserm)
摘要：Kingman's (1978) representation theorem (J. Lond. Math. Soc. (2) 18 (1978) 374-380) states that any exchangeable partition of N can be represented as a paintbox based on a random mass-partition. Similarly, any exchangeable composition (i.e., ordered partition of N) can be represented as a paintbox based on an interval-partition (Gnedin (1997) Ann. Probab. 25 (1997) 1437-1450). Our first main result is that any exchangeable coalescent process (not necessarily Markovian) can be represented as a ...
-
作者：Cao, Sky
作者单位：Stanford University
摘要：For random combinatorial optimization problems, there has been much progress in establishing laws of large numbers and computing limiting constants for the optimal values of various problems. However, there has not been as much success in proving central limit theorems. This paper introduces a method for establishing central limit theorems in the sparse graph setting. It works for problems that display a key property which has been variously called endogeny, long-range independence and replica...
-
作者：Gnewuch, Michael; Hebbinghaus, Nils
作者单位：University Osnabruck; University of Kiel
摘要：We introduce a class of gamma-negatively dependent random samples. We prove that this class includes, apart from Monte Carlo samples, in particular Latin hypercube samples and Latin hypercube samples padded by Monte Carlo. For a gamma-negatively dependent N-point sample in dimension d we provide probabilistic upper bounds for its star discrepancy with explicitly stated dependence on N, d, and gamma. These bounds generalize the probabilistic bounds for Monte Carlo samples from Heinrich et al. (...
-
作者：Diaconis, Persi; Houston-Edwards, Kelsey; Saloff-Coste, Laurent
作者单位：Stanford University; Franklin W. Olin College of Engineering; Cornell University
摘要：Gambler's ruin estimates can be viewed as harmonic measure estimates for finite Markov chains which are absorbed (or killed) at boundary points. We relate such estimates to properties of the underlying chain and its Doob transform. Precisely, we show that gambler's ruin estimates reduce to a good understanding of the Perron-Frobenius eigenfunction and eigenvalue whenever the underlying chain and its Doob transform are Harnack Markov chains. Finite inner-uniform domains (say, in the square grid...
-
作者：Ball, Frank
作者单位：University of Nottingham
摘要：We consider a stochastic SIR (susceptible -> infective -> recovered) epidemic defined on a configuration model random graph, in which infective individuals can infect only their neighbours in the graph during an infectious period which has an arbitrary but specified distribution. Central limit theorems for the final size (number of initial susceptibles that become infected) of such an epidemic as the population size n tends to infinity, with explicit, easy to compute expressions for the asympt...
-
作者：Gan, Han L.; Ross, Nathan
作者单位：Northwestern University; University of Melbourne
摘要：We provide a general theorem bounding the error in the approximation of a random measure of interest-for example, the empirical population measure of types in a Wright-Fisher model-and a Dirichlet process, which is a measure having Poisson-Dirichlet distributed atoms with i.i.d. labels from a diffuse distribution. The implicit metric of the approximation theorem captures the sizes and locations of the masses, and so also yields bounds on the approximation between the masses of the measure of i...
-
作者：Sun, Jingrui; Xiong, Jie; Yong, Jiongmin
作者单位：Southern University of Science & Technology; State University System of Florida; University of Central Florida
摘要：This paper is concerned with a stochastic linear-quadratic optimal control problem in a finite time horizon, where the coefficients of the control system are allowed to be random, and the weighting matrices in the cost functional are allowed to be random and indefinite. It is shown, with a Hilbert space approach, that for the existence of an open-loop optimal control, the convexity of the cost functional (with respect to the control) is necessary; and the uniform convexity, which is slightly s...
