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作者：Muirhead, Stephen; Pymar, Richard; Sidorova, Nadia
作者单位：University of Oxford; University of London; University College London; University of London; University College London; University of London; Birkbeck University London
摘要：The parabolic Anderson model on with i.i.d. potential is known to completely localise if the distribution of the potential is sufficiently heavy-tailed at infinity. In this paper we investigate a modification of the model in which the potential is partially duplicated in a symmetric way across a plane through the origin. In the case of potential distribution with polynomial tail decay, we exhibit a surprising phase transition in the model as the decay exponent varies. For large values of the e...
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作者：Ding, Jian; Zhang, Fuxi
作者单位：University of Chicago; Peking University
摘要：We consider first passage percolation (FPP) where the vertex weight is given by the exponential of two-dimensional log-correlated Gaussian fields. Our work is motivated by understanding the discrete analog for the random metric associated with Liouville quantum gravity (LQG), which roughly corresponds to the exponential of a two-dimensional Gaussian free field (GFF). The particular focus of the present paper is an aspect of universality for such FPP among the family of log-correlated Gaussian ...
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作者：Joos, Felix; Perarnau, Guillem; Rautenbach, Dieter; Reed, Bruce
作者单位：University of Birmingham; Ulm University; Centre National de la Recherche Scientifique (CNRS); Research Organization of Information & Systems (ROIS); National Institute of Informatics (NII) - Japan; Instituto Nacional de Matematica Pura e Aplicada (IMPA)
摘要：For a fixed degree sequence , let be a uniformly chosen (simple) graph on where the vertex i has degree . In this paper we determine whether has a giant component with high probability, essentially imposing no conditions on . We simply insist that the sum of the degrees in which are not 2 is at least for some function going to infinity with n. This is a relatively minor technical condition, and when does not satisfy it, both the probability that has a giant component and the probability that h...
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作者：Basrak, Bojan; Planinic, Hrvoje; Soulier, Philippe
作者单位：University of Zagreb; Universite Paris Saclay
摘要：We prove a sequence of limiting results about weakly dependent stationary and regularly varying stochastic processes in discrete time. After deducing the limiting distribution for individual clusters of extremes, we present a new type of point process convergence theorem. It is designed to preserve the entire information about the temporal ordering of observations which is typically lost in the limit after time scaling. By going beyond the existing asymptotic theory, we are able to prove a new...
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作者：Gorin, Vadim; Zhang, Lingfu
作者单位：Massachusetts Institute of Technology (MIT); Kharkevich Institute for Information Transmission Problems of the RAS; Russian Academy of Sciences; Princeton University
摘要：We study the asymptotics of the global fluctuations for the difference between two adjacent levels in the extension of the classical Jacobi ensemble of random matrices). The limit is identified with the derivative of the 2d Gaussian free field. Our main tools are integral forms for the (Macdonald-type) difference operators originating from the shuffle algebra.
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作者：Monmarche, Pierre
作者单位：Institut Polytechnique de Paris; Ecole Nationale des Ponts et Chaussees; Inria; Universite Gustave-Eiffel
摘要：Combining classical arguments for the analysis of the simulated annealing algorithm with the more recent hypocoercive method of distorted entropy, we prove the convergence for large time of the kinetic Langevin annealing with logarithmic cooling schedule.
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作者：Najnudel, Joseph
作者单位：University System of Ohio; University of Cincinnati
摘要：In the present paper, we show that under the Riemann hypothesis, and for fixed h, epsilon > 0, the supremum of the real and the imaginary parts of log.(1/ 2 + i t) for t. [ UT -h, UT + h] are in the interval [(1 -epsilon) log log T, (1 + epsilon) log log T] with probability tending to 1 when T goes to infinity, U being a uniform random variable in [ 0, 1]. This proves a weak version of a conjecture by Fyodorov, Hiary and Keating, which has recently been intensively studied in the setting of ra...
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作者：Avena, L.; Jara, M.; Vollering, F.
作者单位：Leiden University; Leiden University - Excl LUMC; Instituto Nacional de Matematica Pura e Aplicada (IMPA); University of Bath
摘要：We consider a random walk (RW) driven by a simple symmetric exclusion process (SSE). Rescaling the RW and the SSE in such a way that a joint hydrodynamic limit theorem holds we prove a joint path large deviation principle. The corresponding large deviation rate function can be split into two components, the rate function of the SSE and the one of the RW given the path of the SSE. These components have different structures (Gaussian and Poissonian, respectively) and to overcome this difficulty ...
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作者：Biskup, Marek; Koenig, Wolfgang; dos Santos, Renato S.
作者单位：University of California System; University of California Los Angeles; Charles University Prague; Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; Technical University of Berlin
摘要：We study the non-negative solution to the Cauchy problem for the parabolic equation on with initial data . Here is the discrete Laplacian on and is an i.i.d. random field with doubly-exponential upper tails. We prove that, for large t and with large probability, most of the total mass of the solution resides in a bounded neighborhood of a site that achieves an optimal compromise between the local Dirichlet eigenvalue of the Anderson Hamiltonian and the distance to the origin. The processes and...
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作者：Buckley, Jeremiah; Nishry, Alon; Peled, Ron; Sodin, Mikhail
作者单位：Consejo Superior de Investigaciones Cientificas (CSIC); CSIC - Instituto de Ciencia de Materiales de Madrid (ICMM); CSIC - Instituto de Ciencias Matematicas (ICMAT); University of Michigan System; University of Michigan; Tel Aviv University
摘要：We study a family of random Taylor series F(z) = n= 0.nan zn with radius of convergence almost surely 1 and independent, identically distributed complex Gaussian coefficients ; these Taylor series are distinguished by the invariance of their zero sets with respect to isometries of the unit disk. We find reasonably tight upper and lower bounds on the probability that F does not vanish in the disk as . Our bounds take different forms according to whether the non-random coefficients grow, decay o...
