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作者：Doney, R. A.; Rivero, V.
作者单位：University of Manchester
摘要：Let be a real valued L,vy process that is in the domain of attraction of a stable law without centering with norming function As an analogue of the random walk results in Vatutin and Wachtel (Probab Theory Relat Fields 143(1-2):177-217, 2009) and Doney (Probab Theory Relat Fields 152(3-4):559-588, 2012), we study the local behaviour of the distribution of the lifetime under the characteristic measure of excursions away from of the process reflected in its past infimum, and of the first passage...
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作者：Tao, Terence
作者单位：University of California System; University of California Los Angeles
摘要：We show that the distribution of (a suitable rescaling of) a single eigenvalue gap of a random Wigner matrix ensemble in the bulk is asymptotically given by the Gaudin-Mehta distribution, if the Wigner ensemble obeys a finite moment condition and matches moments with the GUE ensemble to fourth order. This is new even in the GUE case, as prior results establishing the Gaudin-Mehta law required either an averaging in the eigenvalue index parameter , or fixing the energy level instead of the eige...
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作者：Meister, Alexander; Reiss, Markus
作者单位：University of Rostock; Humboldt University of Berlin
摘要：Asymptotic equivalence in Le Cam's sense for nonparametric regression experiments is extended to the case of non-regular error densities, which have jump discontinuities at their endpoints. We prove asymptotic equivalence of such regression models and the observation of two independent Poisson point processes which contain the target curve as the support boundary of its intensity function. The intensity of the point processes is of order of the sample size n and involves the jump sizes as well...
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作者：Bauerschmidt, Roland
作者单位：University of British Columbia
摘要：We present a simple method to decompose the Green forms corresponding to a large class of interesting symmetric Dirichlet forms into integrals over symmetric positive semi-definite and finite range (properly supported) forms that are smoother than the original Green form. This result gives rise to multiscale decompositions of the associated Gaussian free fields into sums of independent smoother Gaussian fields with spatially localized correlations. Our method makes use of the finite propagatio...
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作者：Belius, David
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：This work proves that the fluctuations of the cover time of simple random walk in the discrete torus of dimension at least three with large side-length are governed by the Gumbel extreme value distribution. This result was conjectured for example in Aldous and Fill (Reversible Markov chains and random walks on graphs, in preparation). We also derive some corollaries which qualitatively describe how covering happens. In addition, we develop a new and stronger coupling of the model of random int...
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作者：DeBlassie, Dante; Smits, Robert G.
作者单位：New Mexico State University
摘要：Using a solution of a nonhomogeneous partial differential equation involving the p-Laplacian, we study the finiteness of the expected time to end the tug-of-war in a wedge.
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作者：Bloemendal, Alex; Virag, Balint
作者单位：Harvard University; University of Toronto; University of Toronto
摘要：Given a large, high-dimensional sample from a spiked population, the top sample covariance eigenvalue is known to exhibit a phase transition. We show that the largest eigenvalues have asymptotic distributions near the phase transition in the rank one spiked real Wishart setting and its general beta analogue, proving a conjecture of Baik et al. (Ann Probab 33:1643-1697, 2005). We also treat shifted mean Gaussian orthogonal and beta ensembles. Such results are entirely new in the real case; in t...
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作者：Yattselev, Maxim L.
作者单位：University of Oregon
摘要：A two-dimensional statistical model of N charged particles interacting via logarithmic repulsion in the presence of an oppositely charged regular closed region K whose charge density is determined by its equilibrium potential at an inverse temperature beta is investigated. When the charge on the region, s, is greater than N, the particles accumulate in a neighborhood of the boundary of K, and form a point process in the complex plane. We describe the weak* limits of the joint intensities of th...
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作者：Aidekon, E.; Berestycki, J.; Brunet, E.; Shi, Z.
作者单位：Eindhoven University of Technology; Universite Paris Cite; Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Centre National de la Recherche Scientifique (CNRS); Universite PSL; Ecole Normale Superieure (ENS); Universite Paris Cite; Sorbonne Universite
摘要：It has been conjectured since the work of Lalley and Sellke (Ann. Probab., 15, 1052-1061, 1987) that branching Brownian motion seen from its tip (e.g. from its rightmost particle) converges to an invariant point process. Very recently, it emerged that this can be proved in several different ways (see e.g. Brunet and Derrida, A branching random walk seen from the tip, 2010, Poissonian statistics in the extremal process of branching Brownian motion, 2010; Arguin et al., The extremal process of b...
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作者：Ding, Jian
作者单位：Stanford University
摘要：We study the tail behavior for the maximum of discrete Gaussian free field on a 2D box with Dirichlet boundary condition after centering by its expectation. We show that it exhibits an exponential decay for the right tail and a double exponential decay for the left tail. In particular, our result implies that the variance of the maximum is of order 1, improving an bound by Chatterjee (Chaos, concentration, and multiple valleys, 2008) and confirming a folklore conjecture. An important ingredien...
