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作者：Delon, Julie; Gozlan, Nathael; SAINT Dizier, Alexandre
作者单位：Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS)
摘要：In this paper, we introduce a generalization of the Wasserstein barycenter, to a case where the initial probability measures live on different subspaces of R-d. We study the existence and uniqueness of this barycenter, we show how it is related to a larger multimarginal optimal transport problem, and we propose a dual formulation. Finally, we explain how to compute numerically this generalized barycenter on discrete distributions, and we propose an ex-plicit solution for Gaussian distributions.
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作者：Gamarnik, David; Kizildag, Eren c.
作者单位：Massachusetts Institute of Technology (MIT); Columbia University
摘要：We consider the algorithmic problem of finding a near-optimal solution for the number partitioning problem (NPPNPP). This problem appears in many practical applications, including the design of randomized controlled trials, multiprocessor scheduling, and cryptography. It is also of theoretical significance. The NPPNPP possesses a so-called statistical-to-computational gap: when its input X has distribution N(0,In), the optimal value of the NPPNPP is Theta(root n2(-n))w.h.p., whereas the best-k...
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作者：Jara, Milton; Landim, Claudio
摘要：We prove that in dimension d <= 3 a modified density field of a stirring dynamics perturbed by a voter model converges to the stochastic heat equation.
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作者：Li, Yiting
作者单位：Korea Advanced Institute of Science & Technology (KAIST)
摘要：For a beta ensemble on Sigma((N)) = {(x(1),... , x(N)) is an element of R-N |x(1) <= center dot center dot center dot <= x(N)} with real analytic potential and general beta > 0, under the assumption that its equilibrium measure is supported on q intervals where q > 1, we prove the following rigidity property for its particles. 1. In the bulk of the spectrum, with overwhelming probability, the distance between a particle and its classical position is of order O (N-1+epsilon). 2. If k is close t...
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作者：Chenavier, Nicolas; Coupier, David; Rousselle, Arnaud
作者单位：Centre National de la Recherche Scientifique (CNRS)
摘要：We investigate three types of internal diffusion limited aggregation (IDLA) models. These models are based on simple random walks on Z2 with infinitely many sources that are the points of the vertical axis I (infinity) = {0}x Z. Various properties are provided, such as stationarity, mixing, stabilization and shape theorems. Our results allow us to define a new directed (w.r.t. the hor-izontal direction) random forest spanning Z2, based on an IDLA protocol, which is invariant in distribution w....
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作者：Bansaye, Vincent; Gu, Chenlin; Yuan, Linglong
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; Tsinghua University; University of Liverpool
摘要：We consider a random process on recursive trees, with three types of events. Vertices give birth at a constant rate (growth), each edge may be re-moved independently (fragmentation of the tree) and clusters (or trees) are frozen with a rate proportional to their sizes (isolation of connected compo-nent). A phase transition occurs when the isolation is able to stop the growth -fragmentation process and cause extinction. When the process survives, the number of clusters increases exponentially a...
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作者：Bouchard, Bruno; Loeper, Gregoire; Tan, Xiaolu
作者单位：Universite PSL; Universite Paris-Dauphine; Centre National de la Recherche Scientifique (CNRS); Monash University; Monash University; Chinese University of Hong Kong
摘要：We introduce a notion of approximate viscosity solutions for a class of nonlinear path-dependent PDEs (PPDEs), including the Hamilton-Jacobi- Bellman-type equations. Existence, comparaison and stability results have been established under fairly general conditions. It is also consistent with the notion of smooth solution when the dimension is less or equal to two, or the nonlinearity is concave in the second order space derivative. We finally investigate the regularity (in the sense of Dupire)...
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作者：Last, Guenter; Otto, Moritz
作者单位：Helmholtz Association; Karlsruhe Institute of Technology; Aarhus University
摘要：We discuss a thinning and an embedding procedure to construct finite Gibbs processes with a given Papangelou intensity. Extending the approach of Hofer-Temmel (Electron. J. Probab. 24 (2019) 1-22) and Hofer-Temmel and Houdebert (Stochastic Process. Appl. 129 (2019) 3922-3940) we will use this to couple two finite Gibbs processes with different boundary conditions. As one application we will establish Poisson approximation of point processes derived from certain infinite volume Gibbs processes ...
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作者：Klimek, Aleksander; Rosati, Tommaso Cornelis
作者单位：University of Edinburgh; University of Warwick
摘要：We study the large scale behaviour of a population consisting of two types which evolve in dimension d = 1, 2 according to a spatial Lambda-Fleming-Viot process subject to random time-independent selection. If one of the two types is rare compared to the other, we prove that its evolution can be approximated by a super-Brownian motion in a random (and singular) en-vironment. Without the sparsity assumption, a diffusion approximation leads to a Fisher-KPP equation in a random potential. The pro...
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作者：Del Moral, Pierre; Horton, Emma
摘要：Despite the widespread usage of discrete generation ensemble Kalman particle filtering methodology to solve nonlinear and high-dimensional fil-tering and inverse problems, little is known about their mathematical foun-dations. As genetic-type particle filters (a.k.a. sequential Monte Carlo), this ensemble-type methodology can also be interpreted as mean-field particle ap-proximations of the Kalman-Bucy filtering equation. In contrast with conven-tional mean-field type interacting particle meth...
