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作者：Burdzy, Krzysztof
作者单位：University of Washington; University of Washington Seattle
摘要：The meteor process is a model for mass redistribution on a graph. The case of finite graphs was analyzed in Billey et al. (On meteors, earthworms and WIMPs. Ann Appl Probab, 2014). This paper is devoted to the meteor process on . The process is constructed and a stationary distribution is found. Convergence to this stationary distribution is proved for a large family of initial distributions. The first two moments of the mass distribution at a vertex are computed for the stationary distributio...
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作者：Adler, Mark; Chhita, Sunil; Johansson, Kurt; van Moerbeke, Pierre
作者单位：Brandeis University; University of Bonn; Royal Institute of Technology; Universite Catholique Louvain
摘要：We study determinantal point processes arising in random domino tilings of a double Aztec diamond, a region consisting of two overlapping Aztec diamonds. At a turning point in a single Aztec diamond where the disordered region touches the boundary, the natural limiting process is the GUE-minor process. Increasing the size of a double Aztec diamond while keeping the overlap between the two Aztec diamonds finite, we obtain a new determinantal point process which we call the tacnode GUE-minor pro...
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作者：Hilario, M. R.; Sidoravicius, V.; Teixeira, A.
作者单位：Universidade Federal de Minas Gerais; University of Geneva; Instituto Nacional de Matematica Pura e Aplicada (IMPA); Universite PSL; Ecole Normale Superieure (ENS)
摘要：We study the complementary set of a Poissonian ensemble of infinite cylinders in , for which an intensity parameter controls the amount of cylinders to be removed from the ambient space. We establish a non-trivial phase transition, for the existence of an unbounded connected component of this set, as crosses a critical non-degenerate intensity . We moreover show that this complementary set percolates in a sufficiently thick slab, in spite of the fact that it does not percolate in any given pla...
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作者：Adamczak, Radoslaw; Wolff, Pawel
作者单位：University of Warsaw; Polish Academy of Sciences; Institute of Mathematics of the Polish Academy of Sciences
摘要：Building on the inequalities for homogeneous tetrahedral polynomials in independent Gaussian variables due to R. Lataa we provide a concentration inequality for not necessarily Lipschitz functions with bounded derivatives of higher orders, which holds when the underlying measure satisfies a family of Sobolev type inequalities Such Sobolev type inequalities hold, e.g., if the underlying measure satisfies the log-Sobolev inequality (in which case ) or the Poincar, inequality (then ). Our concent...
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作者：Ay, Nihat; Jost, Juergen; Le, Hong Van; Schwachhoefer, Lorenz
作者单位：Max Planck Society; Leipzig University; The Santa Fe Institute; Czech Academy of Sciences; Institute of Mathematics of the Czech Academy of Sciences; Dortmund University of Technology
摘要：Information geometry provides a geometric approach to families of statistical models. The key geometric structures are the Fisher quadratic form and the Amari-Chentsov tensor. In statistics, the notion of sufficient statistic expresses the criterion for passing from one model to another without loss of information. This leads to the question how the geometric structures behave under such sufficient statistics. While this is well studied in the finite sample size case, in the infinite case, we ...
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作者：Guntuboyina, Adityanand; Sen, Bodhisattva
作者单位：University of California System; University of California Berkeley; Columbia University
摘要：We consider the problem of nonparametric estimation of a convex regression function . We study the risk of the least squares estimator (LSE) under the natural squared error loss. We show that the risk is always bounded from above by modulo logarithmic factors while being much smaller when is well-approximable by a piecewise affine convex function with not too many affine pieces (in which case, the risk is at most up to logarithmic factors). On the other hand, when has curvature, we show that n...
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作者：Trevisan, Dario
作者单位：Scuola Normale Superiore di Pisa
摘要：We establish the renormalization property for essentially bounded solutions of the continuity equation associated to bounded variation () fields in Wiener spaces, with values in the associated Cameron-Martin space; thus obtaining, by standard arguments, new uniqueness and stability results for correspondent Lagrangian flows.
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作者：Bogdan, Krzysztof; Grzywny, Tomasz; Ryznar, Micha
作者单位：Polish Academy of Sciences; Institute of Mathematics of the Polish Academy of Sciences; Wroclaw University of Science & Technology
摘要：We give superharmonic functions and derive sharp bounds for the expected exit time and probability of survival for isotropic unimodal L,vy processes in smooth domains.
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作者：Katori, Makoto
作者单位：Chuo University
摘要：We introduce an elliptic extension of Dyson's Brownian motion model, which is a temporally inhomogeneous diffusion process of noncolliding particles defined on a circle. Using elliptic determinant evaluations related to the reduced affine root system of type , we give determinantal martingale representation (DMR) for the process, when it is started at the configuration with equidistant spacing on the circle. DMR proves that the process is determinantal and the spatio-temporal correlation kerne...
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作者：Panchenko, Dmitry
作者单位：Texas A&M University System; Texas A&M University College Station
摘要：The main result in this paper is motivated by the M,zard-Parisi ansatz which predicts a very special structure for the distribution of spins in diluted mean field spin glass models, such as the random -sat model at positive temperature. Using the fact that one can safely assume the validity of the Ghirlanda-Guerra identities in these models, we prove hierarchical exchangeability of pure states for the asymptotic Gibbs measures, which allows us to apply a representation result for hierarchicall...
