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作者：Avena, Luca; Capannol, Federico; Hazra, Rajat subhra; Quattropani, Matteo
作者单位：University of Florence; Leiden University - Excl LUMC; Leiden University; Sapienza University Rome
摘要：We consider the so-called directed configuration model (DCM), that is, a random directed graph with prescribed in- and out-degrees. In this random geometry, we study the meeting time of two random walks starting at stationarity, the coalescence time for a system of coalescent random walks, and the consensus time of the classical voter model. Indeed, it is known that the latter three quantities are related to each other under certain mean field conditions requiring fast enough mixing time and n...
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作者：Jacod, Jean; Lin, Huidi; Todorov, Viktor
作者单位：Sorbonne Universite; Universite Paris Cite; Northwestern University
摘要：In this paper we develop tests for detecting systematic jumps in asset prices of general form, including ones not explained by observable factors, and we further propose nonparametric estimates for them. The inference is based on a panel of high-frequency asset returns, with both the sampling frequency and the size of the cross-section increasing asymptotically. The feasible limit theory developed in the paper utilizes the different asymptotic roles played by diffusive versus jump risks and sy...
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作者：Prodhomme, A. drien; Strickler, Edouard
作者单位：Universite de Tours; Universite de Lorraine; Inria; Centre National de la Recherche Scientifique (CNRS)
摘要：We consider an epidemic SIS model described by a multitype birth-and-death process in a randomly switching environment. That is, the infection and cure rates of the process depend on the state of a finite Markov jump process (the environment), whose transitions also depend on the number of infectives. The total size of the population is constant and equal to some K is an element of N*, and the number of infectives vanishes almost surely in finite time. We prove that, as K -> infinity, the proc...
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作者：Stannat, Wilhelm; Wessels, Lukas
作者单位：Technical University of Berlin; University System of Georgia; Georgia Institute of Technology
摘要：Using a recently introduced representation of the second order adjoint state as the solution of a function-valued backward stochastic partial differential equation (SPDE), we calculate the viscosity super- and subdifferential of the value function evaluated along an optimal trajectory for controlled semilinear SPDEs. This establishes the well-known connection between Pontryagin's maximum principle and dynamic programming within the framework of viscosity solutions. As a corollary, we derive th...
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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...
