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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...
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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：Carlier, Guillaume; Friesecke, Gero; Voegler, Daniela
作者单位：Universite PSL; Universite Paris-Dauphine; Technical University of Munich
摘要：We present a novel analogue for finite exchangeable sequences of the de Finetti, Hewitt and Savage theorem and investigate its implications for multi-marginal optimal transport (MMOT) and Bayesian statistics. If (Z(1), ..., Z(N)) is a finitely exchangeable sequence of N random variables taking values in some Polish space X, we show that the law mu(k) of the first k components has a representation of the form mu(k )= integral F-P1/N(X) (N,k)(lambda) d alpha(lambda) for some probability measure ...
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作者：Aldous, David; Contat, Alice; Curien, Nicolas; Henard, Olivier
作者单位：University of California System; University of California Berkeley; Universite Paris Saclay
摘要：Let (A(u) : u is an element of B) be i.i.d. non-negative integers that we interpret as car arrivals on the vertices of the full binary tree B. Each car tries to park on its arrival node, but if it is already occupied, it drives towards the root and parks on the first available spot. It is known (Bahl et al. in Parking on supercritical Galton-Watson trees, arXiv:1912.13062, 2019; Goldschmidt and Przykucki in Comb Probab Comput 28:23-45, 2019) that the parking process on B exhibits a phase trans...
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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：Birkner, Matthias; Greven, Andreas; den Hollander, Frank
作者单位：Johannes Gutenberg University of Mainz; University of Erlangen Nuremberg; Leiden University; Leiden University - Excl LUMC
摘要：In the article Quenched large deviation principle for words in a letter sequence, Probab. Theory Relat. Fields 148, no. 3/4 (2010), 403-456 we derived a quenched large deviation principle for the empirical process of words obtained by cutting an i.i.d. sequence of letters according to an independent renewal process. We derived a representation of the associated rate function for stationary word processes in terms of certain specific relative entropies. Our proof of this representation is corre...
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作者：Augeri, Fanny; Butez, Raphael; Zeitouni, Ofer
作者单位：Weizmann Institute of Science; Universite Paris Cite; Universite de Lille; New York University
摘要：We prove a central limit theorem for the real part of the logarithm of the characteristic polynomial of random Jacobi matrices. Our results cover the G beta E models for beta > 0.
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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...
