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作者：Mousset, Frank; Noever, Andreas; Panagiotou, Konstantinos; Samotij, Wojciech
作者单位：Tel Aviv University; Swiss Federal Institutes of Technology Domain; ETH Zurich; University of Munich
摘要：Given a hypergraph Gamma = (Omega, chi) and a sequence p = (p(omega))(omega is an element of)(Q) of values in (0, 1), let Omega(p) be the random subset of Omega obtained by keeping every vertex omega independently with probability p(omega). We investigate the general question of deriving fine (asymptotic) estimates for the probability that Omega(p) is an independent set in Gamma, which is an omnipresent problem in probabilistic combinatorics. Our main result provides a sequence of upper and lo...
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作者：Jara, Milton; Menezes, Otavio
作者单位：Instituto Nacional de Matematica Pura e Aplicada (IMPA); Universidade de Lisboa
摘要：We establish an invariance principle for a one-dimensional random walk in a dynamic random environment given by a speed-change exclusion process. The jump probabilities of the walk depend on the configuration of the exclusion in a finite box around the walker. The environment starts from equilibrium. After a suitable space-time rescaling, the random walk converges to a sum of two independent processes: a Brownian motion and a Gaussian process with stationary increments.
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作者：Blondel, Oriane; Hilario, Marcelo R.; Teixeira, Augusto
作者单位：Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet; CNRS - National Institute for Mathematical Sciences (INSMI); Universidade Federal de Minas Gerais; Instituto Nacional de Matematica Pura e Aplicada (IMPA)
摘要：In this paper, we study random walks on dynamical random environments in 1 + 1 dimensions. Assuming that the environment is invariant under space-time shifts and fulfills a mild mixing hypothesis, we establish a law of large numbers and a concentration inequality around the asymptotic speed. The mixing hypothesis imposes a polynomial decay rate of covariances on the environment with sufficiently high exponent but does not impose uniform mixing. Examples of environments for which our methods ap...
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作者：Chiarini, Alberto; Nitzschner, Maximilian
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We investigate percolation of the vacant set of random interlacements on Z(d), d >= 3, in the strongly percolative regime. We consider the event that the interlacement set at level u disconnects the discrete blow-up of a compact set A subset of R-d from the boundary of an enclosing box. We derive asymptotic large deviation upper bounds on the probability that the local averages of the occupation times deviate from a specific function depending on the harmonic potential of A, when disconnection...
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作者：Nadtochiy, Sergey; Shkolnikov, Mykhaylo
作者单位：Illinois Institute of Technology; Princeton University; Princeton University
摘要：Building on the line of work (Ann. Appl. Probab. 25 (2015) 2096-2133; Stochastic Process. Appl. 125 (2015) 2451-2492; Ann. Appl. Probab. 29 (2019) 89-129; Arch. Ration. Mech. Anal. 233 (2019) 643-699; Ann. Appl. Probab. 29 (2019) 2338-2373; Finance Stoch. 23 (2019) 535-594), we continue the study of particle systems with singular interaction through hitting times. In contrast to the previous research, we (i) consider very general driving processes and interaction functions, (ii) allow for inho...
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作者：Alt, Johannes; Erdos, Laszlo; Krueger, Torben; Schroeder, Dominik
作者单位：University of Geneva; Institute of Science & Technology - Austria; University of Bonn
摘要：We prove edge universality for a general class of correlated real symmetric or complex Hermitian Wigner matrices with arbitrary expectation. Our theorem also applies to internal edges of the self-consistent density of states. In particular, we establish a strong form of band rigidity which excludes mismatches between location and label of eigenvalues close to internal edges in these general models.
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作者：Bates, Erik; Chatterjee, Sourav
作者单位：University of California System; University of California Berkeley; Stanford University
摘要：For a broad class of Gaussian disordered systems at low temperature, we show that the Gibbs measure is asymptotically localized in small neighborhoods of a small number of states. From a single argument, we obtain: (i) a version of complete path localization for directed polymers that is not available even for exactly solvable models, and (ii) a result about the exhaustiveness of Gibbs states in spin glasses not requiring the Ghirlanda-Guerra identities.
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作者：Caravenna, Francesco; Sun, Rongfeng; Zygouras, Nikos
作者单位：University of Milano-Bicocca; National University of Singapore; University of Warwick
摘要：We consider the KPZ equation in space dimension 2 driven by spacetime white noise. We showed in previous work that if the noise is mollified in space on scale epsilon and its strength is scaled as (beta) over cap/root vertical bar log epsilon vertical bar, then a transition occurs with explicit critical point (beta) over cap (c) = root 2 pi. Recently Chatterjee and Dunlap showed that the solution admits subsequential scaling limits as epsilon down arrow 0, for sufficiently small (beta) over ca...
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作者：Hong, Jieliang; Mytnik, Leonid; Perkins, Edwin
作者单位：University of British Columbia; Technion Israel Institute of Technology
摘要：We show that if partial derivative R is the boundary of the range of super-Brownian motion and dim denotes Hausdorff dimension, then with probability one, for any open set U, U boolean AND partial derivative R. not equal empty set implies dim(U boolean AND partial derivative R) = {4-2 root 2 approximate to 1.17 if d = 2, 9 - root 17/2 approximate to 2.44 if d = 3. This improves recent results of the last two authors by working with the actual topological boundary, rather than the boundary of t...
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作者：Chatterjee, Sourav; Dunlap, Alexander
作者单位：Stanford University; Stanford University
摘要：The (d + 1)-dimensional KPZ equation is the canonical model for the growth of rough d-dimensional random surfaces. A deep mathematical understanding of the KPZ equation for d = 1 has been achieved in recent years, and the case d >= 3 has also seen some progress. The most physically relevant case of d = 2, however, is not very well understood mathematically, largely due to the renormalization that is required: in the language of renormalization group analysis, the d = 2 case is neither ultravio...
