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作者：Nguyen, Hoi H.
作者单位：University System of Ohio; Ohio State University
摘要：Let X be a matrix sampled uniformly from the set of doubly stochastic matrices of size n x n. We show that the empirical spectral distribution of the normalized matrix root n(X - EX) converges almost surely to the circular law. This confirms a conjecture of Chatterjee, Diaconis and Sly.
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作者：Alberts, Tom; Khanin, Konstantin; Quastel, Jeremy
作者单位：California Institute of Technology; University of Toronto
摘要：We introduce a new disorder regime for directed polymers in dimension 1 + 1 that sits between the weak and strong disorder regimes. We call it the intermediate disorder regime. It is accessed by scaling the inverse temperature parameter beta to zero as the polymer length n tends to infinity. The natural choice of scaling is beta(n) :=beta n(-1/4). We show that the polymer measure under this scaling has previously unseen behavior. While the fluctuation exponents of the polymer endpoint and the ...
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作者：Denis, Laurent; Matoussi, Anis; Zhang, Jing
作者单位：Universite Paris Saclay; Le Mans Universite; Institut Polytechnique de Paris; Ecole Polytechnique
摘要：We prove an existence and uniqueness result for quasilinear Stochastic PDEs with obstacle (OSPDE in short). Our method is based on analytical technics coming from the parabolic potential theory. The solution is expressed as a pair (u, v) where u is a predictable continuous process which takes values in a proper Sobolev space and v is a random regular measure satisfying the minimal Skohorod condition.
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作者：Mackey, Lester; Jordan, Michael I.; Chen, Richard Y.; Farrell, Brendan; Tropp, Joel A.
作者单位：Stanford University; University of California System; University of California Berkeley; University of California System; University of California Berkeley; California Institute of Technology
摘要：This paper derives exponential concentration inequalities and polynomial moment inequalities for the spectral norm of a random matrix. The analysis requires a matrix extension of the scalar concentration theory developed by Sourav Chatterjee using Stein's method of exchangeable pairs. When applied to a sum of independent random matrices, this approach yields matrix generalizations of the classical inequalities due to Hoeffding, Bernstein, Khintchine and Rosenthal. The same technique delivers b...
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作者：Handa, Kenji
作者单位：Saga University
摘要：We identify stationary distributions of generalized Fleming-Viot processes with jump mechanisms specified by certain beta laws together with a parameter measure. Each of these distributions is obtained from normalized stable random measures after a suitable biased transformation followed by mixing by the law of a Dirichlet random measure with the same parameter measure. The calculations are based primarily on the well-known relationship to measure-valued branching processes with immigration.
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作者：Adler, Robert J.; Moldavskaya, Elina; Samorodnitsky, Gennady
作者单位：Technion Israel Institute of Technology; Cornell University
摘要：The structure of Gaussian random fields over high levels is a well researched and well understood area, particularly if the field is smooth. However, the question as to whether or not two or more points which lie in an excursion set belong to the same connected component has constantly eluded analysis. We study this problem from the point of view of large deviations, finding the asymptotic probabilities that two such points are connected by a path laying within the excursion set, and so belong...
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作者：Auffinger, Antonio; Damron, Michael
作者单位：University of Chicago; Princeton University
摘要：In a recent breakthrough work, Chatterjee [Ann. of Math. (2) 177 (2013) 663-697] proved a long standing conjecture that relates the transversal exponent and the fluctuation exponent x in first-passage percolation on Z(d). The purpose of this paper is to replace the main argument of Chatterjee (2013) and give an alternative proof of this relation. Specifically, we show that under the assumption that exponents defined in Chatterjee (2013) exist, one has the relation x <= 2 xi - 1. One advantage ...
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作者：Aidekon, Elie; Shi, Zhan
作者单位：Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We consider the boundary case (in the sense of Biggins and Kyprianou [Electron. J. Probab. 10 (2005) 609-631] in a one-dimensional supercritical branching random walk, and study the additive martingale (W-n). We prove that, upon the system's survival, n(1/2)W(n) converges in probability, but not almost surely, to a positive limit. The limit is identified as a constant multiple of the almost sure limit, discovered by Biggins and Kyprianou, of the derivative martingale.
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作者：Andjel, E. D.
作者单位：Aix-Marseille Universite
摘要：We study subcritical two-dimensional oriented percolation seen from its rightmost point on the set of infinite configurations which are bounded above. This a Feller process whose state space is not compact and has no invariant measures. We prove that it converges in distribution to a measure which charges only finite configurations.
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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 Parisi formula for the free energy in the Sherrington-Kirkpatrick and mixed p-spin models for even p >= 2 was proved in the seminal work of Michel Talagrand [Ann. of Math. (2) 163 (2006) 221-263]. In this paper we prove the Parisi formula for general mixed p-spin models which also include p-spin interactions for odd p. Most of the ideas used in the paper are well known and can now be combined following a recent proof of the Parisi ultrametricity conjecture in.
