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作者：Manole, Tudor; Niles-Weed, Jonathan
作者单位：Carnegie Mellon University; New York University
摘要：We revisit the question of characterizing the convergence rate of plug-in estimators of optimal transport costs. It is well known that an empirical measure comprising independent samples from an absolutely continuous distribution on R-d converges to that distribution at the rate n(-1/d) in Wasserstein distance, which can be used to prove that plug-in estimators of many optimal transport costs converge at this same rate. However, we show that when the cost is smooth, this analysis is loose: plu...
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作者：Flammant, Lucas
作者单位：Universite Polytechnique Hauts-de-France; Centre National de la Recherche Scientifique (CNRS)
摘要：The Euclidean directed spanning forest is a random forest in Rd introduced by Baccelli and Bordenave in 2007 and we introduce and study here the analogous tree in the hyperbolic space. The topological properties of the Euclidean DSF have been stated for d = 2 and conjectured for d = 3 (see further): it should be a tree for d is an element of{2, 3} and a countable union of disjoint trees for d >= 4. Moreover, it should not contain bi-infinite branches whatever the dimension d. In this paper, we...
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作者：Li, Liping; Sun, Wenjie
作者单位：Fudan University; Tongji University
摘要：In this paper we study a stiff problem in two-dimensional space and especially characterize its probabilistic counterpart. More specifically, consider the heat equation with a parameter epsilon > 0: partial derivative(t)u(epsilon)(t,x) = 1/2 del (A(epsilon) (x)del u(epsilon)(t,x)), t >= 0 , x is an element of R-2, where A(epsilon) (x) := Id(2), the identity matrix, for x is not an element of Omega(epsilon) := { x = (x(1),x(2)) is an element of R-2: |x(2) | < epsilon } and A(epsilon) (x) := (a(...
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作者：Zheng, Xinghua; Zhu, Qingsan
作者单位：Hong Kong University of Science & Technology; Hong Kong University of Science & Technology
摘要：We study supercritical spatial SIR epidemics on Z2 2 x { 1 , 2 ,.. .,N } , where each site in Z2 2 represents a village and N stands for the village size. We establish several asymptotic results as N-* oc . In particular, we derive the probability that the epidemic will last forever if the epidemic is started by one infected individual.E Moreover, we show that, conditional on that the epidemic lasts forever, the epidemic spreads out linearly in all directions and derive an explicit formula for...
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作者：Baccelli, Francois; Haji-Mrsadeghi, Mir -Omid; Haniha, Sayeh k
作者单位：Inria; Sharif University of Technology
摘要：The Doeblin graph of a countable state space Markov chain describes the joint pathwise evolutions of the Markov dynamics starting from all possible initial conditions, with two paths coalescing when they reach the same point of the state space at the same time. Its bridge Doeblin subgraph only contains the paths starting from a tagged point of the state space at all possible times. In the irreducible, aperiodic, and positive recurrent case, the following results are known: the bridge Doeblin g...
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作者：Bensoussan, Alain; Graber, P. Jameson; Yam, Sheung Chi Phillip
作者单位：University of Texas System; University of Texas Dallas; Baylor University; Chinese University of Hong Kong
摘要：We propose a new approach to studying classical solutions of the second order Bellman equation and master equation for mean field type control problems, using a novel form of the lifting idea introduced by P.-L. Lions. Rather than studying the usual system of Hamilton-Jacobi/Fokker-Planck PDEs using analytic techniques, we instead study a stochastic control problem on a specially constructed Hilbert space, which is reminiscent of a tangent space on the Wasserstein space in optimal transport. O...
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作者：Bruned, Yvain; Nadeem, Usama
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Lorraine; University of Edinburgh; Heriot Watt University
摘要：In this work, we show a convergence result for the discrete formulation of the generalised KPZ equation Bt u = (Au) +g(u)(Vu)2 +k(Vu) +h(u) + f (u)xi t(x), where xi is real -valued, A is the discrete Laplacian, and V is a discrete gradient, without fixing the spatial dimension. Our convergence result is established within the discrete regularity structures introduced by Hairer and Erhard (Ann. Inst. Henri Poincare Probab. Stat. 55 (2019) 2209-2248). We extend with new ideas the convergence res...
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作者：Wolfer, Geoffrey; Kontorovich, Aryeh
作者单位：RIKEN; Ben-Gurion University of the Negev
摘要：We show that the minimax sample complexity for estimating the pseudo spectral gap gamma(ps) of an ergodic Markov chain in constant multiplicative error is of the order of (Theta) over tilde (1/gamma(ps)pi(star)), where pi(star) is the minimum stationary probability, recovering the known bound in the reversible setting for estimating the absolute spectral gap (Hsu et al., Ann. Appl. Probab. 29 (2019) 2439-2480), and resolving an open problem of Wolfer and Kontorovich (In Proceedings of the Thir...
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作者：Bayraktar, Erhan; Guo, Gaoyue; Tang, Wenpin; Zhang, Yuming Paul
作者单位：University of Michigan System; University of Michigan; Universite Paris Saclay; Universite Paris Saclay; Columbia University; University of California System; University of California San Diego
摘要：This paper is concerned with the analysis of blow-ups for two McKean-Vlasov equations involving hitting times. Let (B(t); t >= 0) be standard Brownian motion, and tau := inf{t >= 0 : X(t) <= 0} be the hitting time to zero of a given process X. The first equation is X(t) = X(0-) + B(t) - alpha P(tau <= t). We provide a simple condition on a and the distribution of X(0-) such that the corresponding Fokker-Planck equation has no blow-up, and thus the McKean-Vlasov dynamics is well defined for all...
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作者：Ferrari, Patrik; Occelli, Alessandra
作者单位：University of Bonn; Universite d'Angers
摘要：This article studies several properties of the half-space last passage percolation, in particular the two-time covariance. We show that, when the two end-points are at small macroscopic distance, then the first-order correction to the covariance for the point-to-point model is the same as the one of the stationary model. In order to obtain the result, we first derive comparison inequalities of the last passage increments for different models. This is used to prove tightness of the point-to-poi...
