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作者：Berestycki, Nathanael; Lis, Marcin; Qian, Wei
作者单位：University of Vienna; Technische Universitat Wien; City University of Hong Kong
摘要：We study the dimer model on subgraphs of the square lattice in which vertices on a prescribed part of the boundary (the free boundary) are possibly unmatched. Each such unmatched vertex is called a monomer and contributes a fixed multiplicative weight z > 0 to the total weight of the configuration. A bijection described by Giuliani et al. (J Stat Phys 163(2):211-238, 2016) relates this model to a standard dimer model but on a non-bipartite graph. The Kasteleyn matrix of this dimer model descri...
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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：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：Elboim, Dor; Klartag, Bo'az
作者单位：Institute for Advanced Study - USA; Weizmann Institute of Science
摘要：We show that for any set A subset of [0, 1](n) with Vol(A) >= 1/2 there exists a line L such that the one-dimensional Lebesgue measure of L boolean AND A is at least Omega (n(1/4)). The exponent 1/4 is tight. More generally, for a probability measure mu on R-n and 0 < a < 1 define L(mu, a) := inf(A; mu(A)=a) sup(line) vertical bar L boolean AND A vertical bar where vertical bar center dot vertical bar stands for the one-dimensional Lebesgue measure. We study the asymptotic behavior of L(mu, a)...
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作者：Calka, Pierre; Quilan, Gauthier
作者单位：Universite de Rouen Normandie
摘要：The convex hull peeling of a point set is obtained by taking the convex hull of the set and repeating iteratively the operation on the interior points until no point remains. The boundary of each hull is called a layer. We study the number of k-dimensional faces and the outer defect intrinsic volumes of the first layers of the convex hull peeling of a homogeneous Poisson point process in the unit ball whose intensity goes to infinity. More precisely we provide asymptotic limits for their expec...
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作者：Cavagnari, Giulia; Savare, Giuseppe; Sodini, Giacomo Enrico
作者单位：Polytechnic University of Milan; Bocconi University; Bocconi University
摘要：We introduce and investigate a notion of multivalued lambda-dissipative probability vector field (MPVF) in the Wasserstein space P-2(X) of Borel probability measures on a Hilbert space X. Taking inspiration from the theories of dissipative operators in Hilbert spaces and of Wasserstein gradient flows for geodesically convex functionals, we study local and global well posedness of evolution equations driven by dissipative MPVFs. Our approach is based on a measure-theoretic version of the Explic...
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作者：Blumenthal, Alex; Engel, Maximilian; Neamtu, Alexandra
作者单位：University System of Georgia; Georgia Institute of Technology; Free University of Berlin; University of Konstanz
摘要：We investigate pitchfork bifurcations for a stochastic reaction diffusion equation perturbed by an infinite-dimensional Wiener process. It is well-known that the random attractor is a singleton, independently of the value of the bifurcation parameter; this phenomenon is often referred to as the destruction of the bifurcation by the noise. Analogous to the results of Callaway et al. (AIHP Prob Stat 53:1548-1574, 2017) for a 1D stochastic ODE, we show that some remnant of the bifurcation persist...
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作者：Durhuus, Bergfinnur; Unel, Meltem
作者单位：University of Copenhagen
摘要：We consider planar rooted random trees whose distribution is even for fixed height h and size N and whose height dependence is of exponential form e(-mu h). Defining the total weight for such trees of fixed size to be Z((mu)) (N) , we determine its asymptotic behaviour for large N, for arbitrary real values of mu. Based on this we identify the local limit of the corresponding probability measures and find a transition at mu = 0 from a single spine phase to a multi-spine phase. Correspondingly,...
