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作者：Andres, Sebastian; Chiarini, Alberto; Slowik, Martin
作者单位：University of Manchester; Eindhoven University of Technology; University of Mannheim
摘要：We establish a quenched local central limit theorem for the dynamic random conductance model on Z(d) only assuming ergodicity with respect to space-time shifts and a moment condition. As a key analytic ingredient we show Holder continuity estimates for solutions to the heat equation for discrete finite difference operators in divergence form with time-dependent degenerate weights. The proof is based on De Giorgi's iteration technique. In addition, we also derive a quenched local central limit ...
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作者：Benigni, Lucas
作者单位：Universite Paris Cite
摘要：We exhibit new functions of the eigenvectors of the Dyson Brownian motion which follow an equation similar to the Bourgade-Yau eigenvector moment flow (Bourgade and Yau in Commun Math Phys 350(1):231-278, 2017). These observables can be seen as a Fermionic counterpart to the original (Bosonic) ones. By analyzing both Fermionic and Bosonic observables, we obtain new correlations between eigenvectors: (i) The fluctuations n-ary sumation Sigma(alpha is an element of I)|uk(alpha)|2-|I|/N decorrela...
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作者：Ebrahimnejad, Farzam; Lee, James R.
作者单位：University of Washington; University of Washington Seattle
摘要：Consider an infinite planar graph with uniform polynomial growth of degree d > 2. Many examples of such graphs exhibit similar geometric and spectral properties, and it has been conjectured that this is necessary. We present a family of counterexamples. In particular, we show that for every rational d > 2, there is a planar graph with uniform polynomial growth of degree d on which the random walk is transient, disproving a conjecture of Benjamini (Coarse Geometry and Randomness, Volume 2100 of...
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作者：Fyodorov, Yan V.; Muirhead, Stephen
作者单位：University of London; King's College London; University of Melbourne
摘要：We study a random permutation of a lattice box in which each permutation is given a Boltzmann weight with energy equal to the total Euclidean displacement. Our main result establishes the band structure of the model as the box-size N tends to infinity and the inverse temperature beta tends to zero; in particular, we show that the mean displacement is of order min{1/beta,N}. In one dimension our results are more precise, specifying leading-order constants and giving bounds on the rates of conve...
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作者：Haas, Benedicte; Stephenson, Robin
作者单位：Universite Paris 13; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); University of Sheffield; University of Sheffield
摘要：We introduce multi-type Markov Branching trees, which are simple random population tree models where individuals are characterized by their size and their type and give rise to (size,type)-children in a Galton-Watson fashion, with the rule that the size of any individual is at least the sum of the sizes of its children. Assuming that the macroscopic size-splittings are rare, we describe the scaling limits of multi-type Markov Branching trees in terms of multi-type self-similar fragmentation tr...
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作者：Garban, Christophe; Holden, Nina; Sepulveda, Avelio; Sun, Xin
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet; Institut Universitaire de France; Swiss Federal Institutes of Technology Domain; ETH Zurich; Universidad de Chile; University of Pennsylvania
摘要：We construct and analyze a continuum dynamical percolation process which evolves in a random environment given by a gamma-Liouville measure. The homogeneous counterpart of this process describes the scaling limit of discrete dynamical percolation on the rescaled triangular lattice. Our focus here is to study the same limiting dynamics, but where the speed of microscopic updates is highly inhomogeneous in space and is driven by the gamma-Liouville measure associated with a two-dimensional log-c...
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作者：Herold, Felix; Hug, Daniel; Thale, Christoph
作者单位：Helmholtz Association; Karlsruhe Institute of Technology; Ruhr University Bochum
摘要：Poisson processes in the space of (d - 1)-dimensional totally geodesic subspaces (hyperplanes) in a d-dimensional hyperbolic space of constant curvature -1 are studied. The k-dimensional Hausdorff measure of their k-skeleton is considered. Explicit formulas for first- and second-order quantities restricted to bounded observation windows are obtained. The central limit problem for the k-dimensional Hausdorff measure of the k-skeleton is approached in two different set-ups: (i) for a fixed windo...
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作者：Dembo, Amir; Gheissari, Reza
作者单位：Stanford University; Stanford University; University of California System; University of California Berkeley; University of California System; University of California Berkeley
摘要：Consider (X-i (t)) solving a system of N stochastic differential equations interacting through a random matrix J = (J(ij)) with independent (not necessarily identically distributed) random coefficients. We show that the trajectories of averaged observables of (X-i (t)), initialized from some mu independent of J, are universal, i.e., only depend on the choice of the distribution J through its first and second moments (assuming e.g., sub-exponential tails). We take a general combinatorial approa...
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作者：He, Yukun; Knowles, Antti
作者单位：University of Zurich; University of Geneva
摘要：We consider a class of sparse random matrices which includes the adjacency matrix of the Erdos-Renyi graph G(N, p). We show that if N-epsilon <= Np <= N1/3-epsilon then all nontrivial eigenvalues away from 0 have asymptotically Gaussian fluctuations. These fluctuations are governed by a single random variable, which has the interpretation of the total degree of the graph. This extends the result (Huang et al. in Ann Prob 48:916-962, 2020) on the fluctuations of the extreme eigenvalues from Np ...
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作者：Lees, Benjamin; Taggi, Lorenzo
作者单位：University of Bristol; University of Bristol; Sapienza University Rome
摘要：We prove exponential decay of transverse correlations in the Spin O(N) model for arbitrary non-zero values of the external magnetic field and arbitrary spin dimension N > 1. Our result is new when N > 3, in which case no Lee-Yang theorem is available, it is an alternative to Lee-Yang when N = 2, 3, and also holds for a wide class of multi-component spin systems with continuous symmetry. The key ingredients are a representation of the model as a system of coloured random paths, a 'colour-switch...
