-
作者：Georgiou, Nicholas; Wade, Andrew R.
作者单位：Durham University
摘要：Motivated by nanoscale growth of ultra-thin films, we study a model of deposition, on an interval substrate, of particles that perform Brownian mo-tions until any two meet, when they nucleate to form a static island, which acts as an absorbing barrier to subsequent particles. This is a continuum ver-sion of a lattice model studied in the applied literature. We show that the associated interval-splitting process converges in the sparse deposition limit to a Markovian process (in the vein of Bre...
-
作者：Bai, Tianyi; Wan, Yijun
作者单位：New York University; NYU Shanghai; Universite PSL; Ecole Normale Superieure (ENS)
摘要：By introducing a new measure for the infinite Galton-Watson process and providing estimates for (discrete) Green's functions on trees, we establish the asymptotic behavior of the capacity of critical branching random walks: in high dimensions d >= 7, the capacity grows linearly; and in the critical dimension d = 6, it grows asymptotically proportional to n/log n.
-
作者：Yasodharan, Sarath; Sundaresan, Rajesh
作者单位：Indian Institute of Science (IISC) - Bangalore
摘要：This paper studies large deviations of a fully coupled finite state meanfield interacting particle system in a fast varying environment. The empirical measure of the particles evolves in the slow time scale and the random environment evolves in the fast time scale. Our main result is the path-space large deviation principle for the joint law of the empirical measure process of the particles and the occupation measure process of the fast environment. This extends previous results known for two ...
-
作者：Carmona, Rene; Lauriere, Mathieu
作者单位：Princeton University
摘要：We propose two numerical methods for the optimal control of McKean- Vlasov dynamics in finite time horizon. Both methods are based on the intro-duction of a suitable loss function defined over the parameters of a neural net-work. This allows the use of machine learning tools, and efficient implemen-tations of stochastic gradient descent in order to perform the optimization. In the first method, the loss function stems directly from the optimal control problem. The second method tackles a gener...
-
作者：Eichinger, Katharina; Gnann, Manuel V.; Kuehn, Christian
作者单位：Universite PSL; Universite Paris-Dauphine; Delft University of Technology; Technical University of Munich
摘要：We investigate the stability of traveling-pulse solutions to the stochastic FitzHugh-Nagumo equations with additive noise. Special attention is given to the effect of small noise on the classical deterministically stable fast traveling pulse. Our method is based on adapting the velocity of the traveling wave by solving a scalar stochastic ordinary differential equation (SODE) and tracking perturbations to the wave meeting a system of a scalar stochastic partial differential equation (SPDE) cou...
-
作者：McGoff, Kevin; Mukherjee, Sayan; Nobel, Andrew B.
作者单位：University of North Carolina; University of North Carolina Charlotte; Duke University; Duke University; Duke University; Duke University; University of North Carolina; University of North Carolina Chapel Hill
摘要：In this paper we consider the posterior consistency of Bayesian inference procedures when the family of models consists of appropriate stochastic processes. Specifically, we suppose that one observes an unknown ergodic process and one has access to a family of models consisting of dependent processes. In this context, we consider Gibbs posterior inference, which is a loss-based generalization of standard Bayesian inference. Our main results characterize the asymptotic behavior of the Gibbs pos...
-
作者：Lachieze-Rey, Raphael; Peccati, Giovanni; Yang, Xiaochuan
作者单位：Universite Paris Cite; University of Luxembourg; Brunel University
摘要：We establish inequalities for assessing the distance between the distribution of a (possibly multidimensional) functional of a Poisson random measure and that of a Gaussian element. Our bounds only involve add-one cost operators at the order one-that we evaluate and compare at two different scales-and are specifically tailored for studying the Gaussian fluctuations of sequences of geometric functionals displaying a form of weak stabilization-see Penrose and Yukich (Ann. Appl. Probab. 11 (2001)...
-
作者：Bukh, Boris; Cox, Christopher
作者单位：Carnegie Mellon University; Iowa State University
摘要：Let W-(n) be the n-letter word obtained by repeating a fixed word W, and let R-n be a random n-letter word over the same alphabet. We show several results about the length of the longest common subsequence (LCS) between W-(n) and R-n; in particular, we show that its expectation is gamma(W)n - O (root n) for an efficiently-computable constant gamma(W). This is done by relating the problem to a new interacting particle system, which we dub frog dynamics. In this system, the particles (frogs) hop...
-
作者：Backhoff-Veraguas, J.; Pammer, G.
作者单位：University of Vienna; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：Under mild regularity assumptions, the transport problem is stable in the following sense: if a sequence of optimal transport plans pi(1), pi(2), ... converges weakly to a transport plan pi, then pi is also optimal (between its marginals). Alfonsi, Corbetta and Jourdain (Ann. Inst. Henri Poincare Probab. Stat. 56 (2020) 1706-1729) asked whether the same property is true for the martingale transport problem. This question seems particularly pressing since martingale transport is motivated by ro...
-
作者：Gonzalez Casanova, Adrian; Miro Pina, Veronica; Siri-Jegousse, Arno
作者单位：Universidad Nacional Autonoma de Mexico; Universidad Nacional Autonoma de Mexico
摘要：We define a new class of Xi-coalescents characterized by a possibly infinite measure over the nonnegative integers. We call them symmetric coalescents since they are the unique family of exchangeable coalescents satisfying a symmetry property on their coagulation rates: they are invariant under any transformation that consists of moving one element from one block to another without changing the total number of blocks. We illustrate the diversity of behaviors of this family of processes by intr...
