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作者：Ahlberg, Daniel
作者单位：Instituto Nacional de Matematica Pura e Aplicada (IMPA)
摘要：Large deviations in the context of first-passage percolation was first studied in the early 1980s by Grimmett and Kesten, and has since been revisited in a variety of studies. However, none of these studies provides a precise relation between the existence of moments of polynomial order and the decay of probability tails. Such a relation is derived in this paper, and is used to strengthen the conclusion of the shape theorem. In contrast to its one-dimensional counterpart-the Hsu-Robbins-Erdos ...
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作者：Petrov, Leonid
作者单位：Northeastern University; Kharkevich Institute for Information Transmission Problems of the RAS
摘要：We study large-scale height fluctuations of random stepped surfaces corresponding to uniformly random lozenge tilings of polygons on the triangular lattice. For a class of polygons (which allows arbitrarily large number of sides), we show that these fluctuations are asymptotically governed by a Gaussian free (massless) field. This complements the similar result obtained in Kenyon [Comm. Math. Phys. 281 (2008) 675-709] about tilings of regions without frozen facets of the limit shape. In our as...
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作者：Goncalves, Patricia; Jara, Milton; Sethuraman, Sunder
作者单位：Universidade do Minho; Instituto Nacional de Matematica Pura e Aplicada (IMPA); University of Arizona
摘要：We consider a class of nearest-neighbor weakly asymmetric mass conservative particle systems evolving on Z, which includes zero-range and types of exclusion processes, starting from a perturbation of a stationary state. When the weak asymmetry is of order O (n(-gamma)) for 1/2 < gamma <= 1, we show that the scaling limit of the fluctuation field, as seen across process characteristics, is a generalized Ornstein-Uhlenbeck process. However, at the critical weak asymmetry when gamma = 1/2, we sho...
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作者：Panchenko, Dmitry
作者单位：University of Toronto
摘要：The authors of [Ann. Henri Poincare 16 (2015) 691-708] introduced a multi-species version of the Sherrington-Kirkpatrick model and suggested the analogue of the Parisi formula for the free energy. Using a variant of Guerra's replica symmetry breaking interpolation, they showed that, under certain assumption on the interactions, the formula gives an upper bound on the limit of the free energy. In this paper we prove that the bound is sharp. This is achieved by developing a new multi-species for...
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作者：Mytnik, Leonid; Wachtel, Vitali
作者单位：Technion Israel Institute of Technology; University of Munich
摘要：We show that density functions of a (alpha, 1, beta)-superprocesses are almost sure multifractal for alpha > beta + 1, beta is an element of (0, 1) and calculate the corresponding spectrum of singularities.
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作者：Dalang, Robert C.; Mueller, Carl
作者单位：Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; University of Rochester
摘要：It is well known that an N-parameter d-dimensional Brownian sheet has no k-multiple points when (k - 1)d > 2kN, and does have such points when (k - 1)d < 2kN. We complete the study of the existence of k-multiple points by showing that in the critical cases where (k - 1)d = 2kN, there are a.s. no k-multiple points.
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作者：Geiss, Stefan; Toivola, Anni
作者单位：University of Jyvaskyla; University of Innsbruck
摘要：We consider Gaussian Besov spaces obtained by real interpolation and Riemann-Liouville operators of fractional integration on the Gaussian space and relate the fractional smoothness of a functional to the regularity of its heat extension. The results are applied to study an approximation problem in L-p for 2 <= p < infinity for stochastic integrals with respect to the d-dimensional (geometric) Brownian motion.
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作者：Kiss, Demeter; Manolescu, Ioan; Sidoravicius, Vladas
作者单位：University of Cambridge; University of Geneva; Instituto Nacional de Matematica Pura e Aplicada (IMPA)
摘要：Self-destructive percolation with parameters p, delta is obtained by taking a site percolation configuration with parameter p, closing all sites belonging to infinite clusters, then opening every closed site with probability delta, independently of the rest. Call theta (p, delta) the probability that the origin is in an infinite cluster in the configuration thus obtained. For two-dimensional lattices, we show the existence of delta > 0 such that, for any p > p(c), theta (p, delta) = 0. This pr...
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作者：Barral, Julien; Kupiainen, Antti; Nikula, Miika; Saksman, Eero; Webb, Christian
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris 13; University of Helsinki
摘要：We study one-dimensional exact scaling lognormal multiplicative chaos measures at criticality. Our main results are the determination of the exact asymptotics of the right tail of the distribution of the total mass of the measure, and an almost sure upper bound for the modulus of continuity of the cumulative distribution function of the measure. We also find an almost sure lower bound for the increments of the measure almost everywhere with respect to the measure itself, strong enough to show ...
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作者：Pitman, Jim; Winkel, Matthias
作者单位：University of California System; University of California Berkeley; University of Oxford
摘要：Some, but not all processes of the form M-t = exp(-xi(t)) for a pure-jump subordinator xi with Laplace exponent Phi arise as residual mass processes of particle 1 (tagged particle) in Bertoin's partition-valued exchangeable fragmentation processes. We introduce the notion of a Markovian embedding of M = (M-t, t >= 0) in a fragmentation process, and we show that for each Phi, there is a unique (in distribution) binary fragmentation process in which M has a Markovian embedding. The identificatio...
