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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...
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作者：Peres, Yuval; Stauffer, Alexandre; Steif, Jeffrey E.
作者单位：Microsoft; University of Bath; Chalmers University of Technology; University of Gothenburg
摘要：We study the behavior of random walk on dynamical percolation. In this model, the edges of a graph are either open or closed and refresh their status at rate while at the same time a random walker moves on at rate 1 but only along edges which are open. On the -dimensional torus with side length , we prove that in the subcritical regime, the mixing times for both the full system and the random walker are up to constants. We also obtain results concerning mean squared displacement and hitting ti...
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作者：Ferrari, Patrik L.; Nejjar, Peter
作者单位：University of Bonn
摘要：We consider the totally asymmetric simple exclusion process with initial conditions and/or jump rates such that shocks are generated. If the initial condition is deterministic, then the shock at time will have a width of order . We determine the law of particle positions in the large time limit around the shock in a few models. In particular, we cover the case where at both sides of the shock the process of the particle positions is asymptotically described by the Airy process. The limiting di...
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作者：Kassel, Adrien; Wu, Wei
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich; Brown University
摘要：When a simply connected domain () is approximated in a good way by embedded connected weighted graphs, we prove that the transfer current matrix (defined on the edges of the graph viewed as an electrical network) converges, up to a local weight factor, to the differential of Green's function on . This observation implies that properly rescaled correlations of the spanning tree model and correlations of minimal subconfigurations in the abelian sandpile model have a universal and conformally cov...
