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作者：Adhikari, Arka; Landon, Benjamin
作者单位：Stanford University; University of Toronto
摘要：We establish high probability estimates on the eigenvalue locations of Brownian motion on the N-dimensional unitary group, as well as estimates on the number of eigenvalues lying in any interval on the unit circle. These estimates are optimal up to arbitrarily small polynomial factors in N. Our results hold at the spectral edges (showing that the extremal eigenvalues are within O(N-2/3+) of the edges of the limiting spectral measure), in the spectral bulk, as well as for times near 4 at which ...
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作者：Assaf, Eran; Buckley, Jeremiah; Feldheim, Naomi
作者单位：Dartmouth College; University of London; King's College London; Bar Ilan University
摘要：We study the variance of the number of zeroes of a stationary Gaussian process on a long interval. We give a simple asymptotic description under mild mixing conditions. This allows us to characterise minimal and maximal growth. We show that a small (symmetrised) atom in the spectral measure at a special frequency does not affect the asymptotic growth of the variance, while an atom at any other frequency results in maximal growth.
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作者：Borga, Jacopo; Holden, Nina; Sun, Xin; Yu, Pu
作者单位：Stanford University; University of Pennsylvania; Swiss Federal Institutes of Technology Domain; ETH Zurich; Massachusetts Institute of Technology (MIT)
摘要：The Baxter permuton is a random probability measure on the unit square which describes the scaling limit of uniform Baxter permutations. We determine an explicit formula for the density of the expectation of the Baxter permuton. This answers a question of Dokos and Pak (Online J Anal Comb 9:12, 2014). We also prove that all pattern densities of the Baxter permuton are strictly positive, distinguishing it from other permutons arising as scaling limits of pattern-avoiding permutations. Our proof...
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作者：Cooperman, William
作者单位：University of Chicago
摘要：We prove a quantitative rate of homogenization for the G equation in a random environment with finite range of dependence. Using ideas from percolation theory, the proof bootstraps a result of Cardaliaguet-Souganidis, who proved qualitative homogenization in a more general ergodic environment.
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作者：Hartarsky, Ivailo; Martinelli, Fabio; Toninelli, Cristina
作者单位：Universite PSL; Universite Paris-Dauphine; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Roma Tre University
摘要：The Fredrickson-Andersen 2-spin facilitated model on Z(d) (FA-2f) is a paradigmatic interacting particle system with kinetic constraints (KCM) featuring dynamical facilitation, an important mechanism in condensed matter physics. In FA-2f a site may change its state only if at least two of its nearest neighbours are empty. Although the process is reversible w.r.t. a product Bernoulli measure, it is not attractive and features degenerate jump rates and anomalous divergence of characteristic time...
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作者：Gonzalez, Isaac; Horton, Emma; Kyprianou, Andreas E.
作者单位：University of Bath; Inria; Centre National de la Recherche Scientifique (CNRS); University of Warwick
摘要：We correct the statements of the non-critical convergence theorems in Gonzalez et al. (Probab Theory Rel Fields, 2022), principally correcting the recursive constants that appear in the limits.
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作者：Auffinger, Antonio; Gorski, Christian
作者单位：Northwestern University
摘要：We study first passage percolation (FPP) with stationary edge weights on Cayley graphs of finitely generated virtually nilpotent groups. Previous works of Benjamini and Tessera (Electron J Probab 20:1-20, 2015) and Cantrell and Furman (Groups Geom Dyn 11(4):1307-1345, 2017) show that scaling limits of such FPP are given by Carnot-Caratheodory metrics on the associated graded nilpotent Lie group. We show a converse, i.e. that for any Cayley graph of a finitely generated nilpotent group, any Car...
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作者：Tikhomirov, Konstantin; Youssef, Pierre
摘要：Consider the switch chain on the set of d-regular bipartite graphs on n vertices with 3 <= d <= n(c), for a small universal constant c > 0. We prove that the chain satisfies a Poincare inequality with a constant of order O(nd); moreover, when d is fixed, we establish a log-Sobolev inequality for the chain with a constant of order O-d(n log n). We show that both results are optimal. The Poincare inequality implies that in the regime 3 <= d <= n(c) the mixing time of the switch chain is at most ...
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作者：Balint, Peter; Bruin, Henk; Terhesiu, Dalia
作者单位：Budapest University of Technology & Economics; MTA-BME Stochastics Research Group; Budapest University of Technology & Economics; University of Vienna; Leiden University; Leiden University - Excl LUMC
摘要：We prove limit laws for infinite horizon planar periodic Lorentz gases when, as time n tends to infinity, the scatterer size rho may also tend to zero simultaneously at a sufficiently slow pace. In particular we obtain a non-standard Central Limit Theorem as well as a Local Limit Theorem for the displacement function. To the best of our knowledge, these are the first results on an intermediate case between the two well studied regimes with superdiffusive root n log n scaling (i) for fixed infi...
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作者：Norris, James; Silvestri, Vittoria; Turner, Amanda
作者单位：University of Cambridge; Sapienza University Rome; University of Leeds
摘要：We study scaling limits of a family of planar random growth processes in which clusters grow by the successive aggregation of small particles. In these models, clusters are encoded as a composition of conformal maps and the location of each successive particle is distributed according to the density of harmonic measure on the cluster boundary, raised to some power. We show that, when this power lies within a particular range, the macroscopic shape of the cluster converges to a disk, but that a...
