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作者：Beltran, J.; Landim, C.
作者单位：Pontificia Universidad Catolica del Peru; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Rouen Normandie
摘要：We presented in Beltran and Landim ( J Stat Phys 140:1065-1114, 2010) Beltran and Landim (J Stat Phys 149:598-618, 2012) an approach to derive the metastable behavior of continuous-time Markov chains. We assumed in these articles that the Markov chains visit points in the time scale in which it jumps among the metastable sets. We replace this condition here by assumptions on the mixing times and on the relaxation times of the chains reflected at the boundary of the metastable sets.
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作者：Mischler, Stephane; Mouhot, Clement; Wennberg, Bernt
作者单位：Universite PSL; Universite Paris-Dauphine; University of Cambridge; Chalmers University of Technology; University of Gothenburg
摘要：This paper is devoted the study of the mean field limit for many-particle systems undergoing jump, drift or diffusion processes, as well as combinations of them. The main results are quantitative estimates on the decay of fluctuations around the deterministic limit and of correlations between particles, as the number of particles goes to infinity. To this end we introduce a general functional framework which reduces this question to the one of proving a purely functional estimate on some abstr...
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作者：Bordenave, Charles; Caputo, Pietro
作者单位：Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Universite Federale Toulouse Midi-Pyrenees (ComUE); Institut National des Sciences Appliquees de Toulouse; Roma Tre University
摘要：Consider the ErdAs-Renyi random graph on vertices where each edge is present independently with probability , with fixed. For large , a typical random graph locally behaves like a Galton-Watson tree with Poisson offspring distribution with mean . Here, we study large deviations from this typical behavior within the framework of the local weak convergence of finite graph sequences. The associated rate function is expressed in terms of an entropy functional on unimodular measures and takes finit...
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作者：De Masi, Anna; Ferrari, Pablo A.; Presutti, Errico
作者单位：University of L'Aquila; University of Buenos Aires; Universidade de Sao Paulo; Gran Sasso Science Institute (GSSI)
摘要：We consider the one dimensional symmetric simple exclusion process with additional births and deaths restricted to a subset of configurations where there is a leftmost hole and a rightmost particle. At a fixed rate birth of particles occur at the position of the leftmost hole and at the same rate, independently, the rightmost particle dies. We prove convergence to a hydrodynamic limit and discuss its relation with a free boundary problem.
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作者：Cancrini, N.; Martinelli, F.; Roberto, C.; Toninelli, C.
作者单位：University of L'Aquila; Roma Tre University; Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS)
摘要：On the rooted -ary tree we consider a - kinetically constrained spin model in which the occupancy variable at each node is re-sampled with rate one from the Bernoulli(p) measure iff all its children are vacant. For this process the following picture was conjectured to hold. As long as is below the percolation threshold the process is ergodic with a finite relaxation time while, for , the process on the infinite tree is no longer ergodic and the relaxation time on a finite regular sub-tree beco...
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作者：Curien, Nicolas; Kortchemski, Igor
作者单位：Centre National de la Recherche Scientifique (CNRS); Sorbonne Universite; Sorbonne Universite; Universite PSL; Ecole Normale Superieure (ENS)
摘要：We study site percolation on Angel and Schramm's uniform infinite planar triangulation. We compute several critical and near-critical exponents, and describe the scaling limit of the boundary of large percolation clusters in all regimes (subcritical, critical and supercritical). We prove in particular that the scaling limit of the boundary of large critical percolation clusters is the random stable looptree of index , which was introduced in Curien and Kortchemski (Random stable looptrees. arX...
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作者：Lalley, Steven P.; Shao, Yuan
作者单位：University of Chicago; University of Chicago
摘要：We consider a branching random walk initiated by a single particle at location in which particles alternately reproduce according to the law of a Galton-Watson process and disperse according to the law of a driftless random walk on the integers. When the offspring distribution has mean the branching process is critical, and therefore dies out with probability . We prove that if the particle jump distribution has mean zero, positive finite variance , and finite moment, and if the offspring dist...
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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：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...
