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作者：Dieuleveut, Daphne
作者单位：Universite Paris Saclay
摘要：We consider a fragmentation of discrete trees where the internal vertices are deleted independently at a rate proportional to their degree. Informally, the associated cut-tree represents the genealogy of the nested connected components created by this process. We essentially work in the setting of Galton-Watson trees with offspring distribution belonging to the domain of attraction of a stable law of index alpha is an element of (1, 2). Our main result is that, for a sequence of such trees T-n...
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作者：Jourdain, Benjamin; Lelievre, Tony; Miasojedow, Blazej
作者单位：Institut Polytechnique de Paris; Ecole Nationale des Ponts et Chaussees; Inria; Institut Polytechnique de Paris; Ecole Nationale des Ponts et Chaussees; University of Warsaw
摘要：We consider the random walk Metropolis algorithm on R-n with Gaussian proposals, and when the target probability measure is the n-fold product of a one-dimensional law. In the limit n -> infinity, it is well known (see [Ann. Appl. Probab. 7 (1997) 110-120]) that, when the variance of the proposal scales inversely proportional to the dimension n whereas time is accelerated by the factor n, a diffusive limit is obtained for each component of the Markov chain if this chain starts at equilibrium. ...
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作者：Billey, Sara; Burdzy, Krzysztof; Pal, Soumik; Sagan, Bruce E.
作者单位：University of Washington; University of Washington Seattle; Michigan State University
摘要：We study a model of mass redistribution on a finite graph. We address the questions of convergence to equilibrium and the rate of convergence. We present theorems on the distribution of empty sites and the distribution of mass at a fixed vertex. These distributions are related to random permutations with certain peak sets.
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作者：Borodin, Alexei; Bufetov, Alexey; Olshanski, Grigori
作者单位：Massachusetts Institute of Technology (MIT); Kharkevich Institute for Information Transmission Problems of the RAS; Russian Academy of Sciences; HSE University (National Research University Higher School of Economics)
摘要：We prove the existence of a limit shape and give its explicit description for certain probability distribution on signatures (or highest weights for unitary groups). The distributions have representation theoretic origin-they encode decomposition on irreducible characters of the restrictions of certain extreme characters of the infinite-dimensional unitary group U (infinity) to growing finite-dimensional unitary subgroups U (N). The characters of U(infinity) are allowed to depend on N. In a sp...
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作者：Brummitt, Charles D.; Chatterjee, Shirshendu; Dey, Partha S.; Sivakoff, David
作者单位：University of California System; University of California Davis; New York University; University of Warwick; University System of Ohio; Ohio State University; University System of Ohio; Ohio State University
摘要：We introduce a new kind of percolation on finite graphs called jigsaw percolation. This model attempts to capture networks of people who innovate by merging ideas and who solve problems by piecing together solutions. Each person in a social network has a unique piece of a jigsaw puzzle. Acquainted people with compatible puzzle pieces merge their puzzle pieces. More generally, groups of people with merged puzzle pieces merge if the groups know one another and have a pair of compatible puzzle pi...
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作者：Kharroubi, Idris; Langrene, Nicolas; Huyen Pham
作者单位：Universite PSL; Universite Paris-Dauphine; Universite Paris Cite
摘要：We propose a new probabilistic numerical scheme for fully nonlinear equation of Hamilton-Jacobi-Bellman (HJB) type associated to stochastic control problem, which is based on the Feynman Kac representation in [Kharroubi and Pham (2014)] by means of control randomization and backward stochastic differential equation with nonpositive jumps. We study a discrete time approximation for the minimal solution to this class of BSDE when the time step goes to zero, which provides both an approximation f...
