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作者：Andres, Sebastian; Prevost, Alexis
作者单位：Braunschweig University of Technology; University of Geneva
摘要：We consider first passage percolation (FPP) with passage times generated by a general class of models with long-range correlations on Zd, d >= 2, including discrete Gaussian free fields, Ginzburg-Landau backward difference phi interface models or random interlacements as prominent examples. We show that the associated time constant is positive, the FPP distance is comparable to the Euclidean distance, and we obtain a shape theorem. We also present two applications for random conductance models...
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作者：Alves, Caio; Teixeira, Augusto
作者单位：United States Department of Energy (DOE); Oak Ridge National Laboratory; Instituto Nacional de Matematica Pura e Aplicada (IMPA)
摘要：In this paper we establish a strong decoupling inequality for the cylinder's percolation process introduced by Tykesson and Windisch ( Probab. Theory Related Fields 154 (2012) 165-191). This model features a very strong dependency structure, making it difficult to study, and this is why such decoupling inequalities are desirable. It is important to notice that the type of dependencies featured by cylinder's percolation is particularly intricate, given that the cylinders have infinite range (un...
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作者：Basile, Giada; Enedetto, Dariob; Bertin, Lorenzo; Caglioti, Emanuele
作者单位：Sapienza University Rome
摘要：Weak solutions to the homogeneous Boltzmann equation with increasing energy have been constructed by Lu and Wennberg. We consider an underlying microscopic stochastic model with binary collisions (Kac's model) and show that these solutions are atypical. More precisely, we prove that the probability of observing these paths is exponentially small in the number of particles and compute the exponential rate. This result is obtained by improving the established large deviation estimates in the can...
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作者：Monmarche, Pierre
作者单位：Sorbonne Universite; Sorbonne Universite; Universite Paris Cite
摘要：Quantitative long-time entropic convergence and short-time regularization are established for an idealized Hamiltonian Monte Carlo chain which alternatively follows an Hamiltonian dynamics for a fixed time and then partially or totally refreshes its velocity with an auto-regressive Gaussian step. These results, in discrete time, are the analogues of similar results for the continuous-time kinetic Langevin diffusion, and the latter can be obtained from our bounds in a suitable limit regime. The...
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作者：Deligiannidis, George; de Bortoli, Valentin; Doucet, Arnaud
作者单位：University of Oxford
摘要：We establish that the iterates of the iterative proportional fitting procedure, also known as Sinkhorn's algorithm and commonly used to solve entropy-regularised optimal transport problems, are stable w.r.t. perturbations of the marginals, uniformly in time. Our result is quantitative and stated in terms of the 1-Wasserstein metric. As a corollary we establish a quantitative stability result for Schrodinger bridges.
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作者：Dimitrov, Evgeni; Murthy, Anushka
作者单位：University of South Carolina System; University of South Carolina Columbia; Stanford University
摘要：We consider the asymmetric simple exclusion process (ASEP) with half-flat initial condition. We show that the one-point marginals of the ASEP height function are described by those of the Airy(2 -> 1) process, introduced by Borodin-Ferrari-Sasamoto in (Comm. Pure Appl. Math. 61 (2008) 1603-1629). This result was conjectured by Ortmann-Quastel-Remenik (Ann. Appl. Probab. 26 (2016) 507-548), based on an informal asymptotic analysis of exact formulas for generating functions of the half-flat ASEP...
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作者：Khoshnevisan, Davar; Kim, Kunwoo; Mueller, Carl
作者单位：Utah System of Higher Education; University of Utah; Pohang University of Science & Technology (POSTECH); University of Rochester
摘要：We consider a generalization of the parabolic Anderson model driven by space-time white noise, also called the stochastic heat equation, on the real line: partial derivative(t) u(t, x) = 1/2 partial derivative(2)(x)u(t, x) + sigma(u(t, x)xi(t, x) for t > 0 and x is an element of R. High peaks of solutions have been extensively studied under the name of intermittency, but less is known about spatial regions between peaks, which we may loosely refer to as valleys. We present two results about th...
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作者：Sadhu, Ritwik; Goldfeld, Ziv; Kato, Kengo
作者单位：Cornell University; Cornell University
摘要：We study statistical inference for the optimal transport (OT) map (also known as the Brenier map) from a known absolutely continuous reference distribution onto an unknown finitely discrete target distribution. We derive limit distributions for the Lp-error with arbitrary p E [1, oc) and for linear functionals of the empirical OT map, together with their moment convergence. The former has a non-Gaussian limit, whose explicit density is derived, while the latter attains asymptotic normality. Fo...
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作者：Koehler, Frederic; Mossel, Elchanan
作者单位：University of Chicago; University of Chicago; Massachusetts Institute of Technology (MIT)
摘要：Arrow's theorem concerns a fundamental problem in social choice theory: given the individual preferences of members of a group, how can they be aggregated to form rational group preferences? Arrow showed that in an election between three or more candidates, there are situations where any voting rule satisfying a small list of natural fairness axioms must produce an apparently irrational intransitive outcome. Furthermore, quantitative versions of Arrow's theorem in the literature show that when...
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作者：Xu, Wei
作者单位：Beijing Institute of Technology
摘要：In this work, several convergence results are established for nearly critical self-excited systems in which event arrivals are described by multivariate marked Hawkes point processes. Under some mild high -frequency assumptions, the rescaled density process behaves asymptotically like a multi -type continuous -state branching process with immigration, which is the unique solution to a multi -dimensional stochastic differential equation with dynamical mechanism similar to that of multivariate H...
