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作者：Chasapsis, Giorgos; Nayar, Piotr; Tkocz, Tomasz
作者单位：Carnegie Mellon University; University of Warsaw
摘要：We show that the two-dimensional minimum-volume central section of the n-dimensional cross-polytope is attained by the regular 2n-gon. We estab-lish stability-type results for hyperplane sections of l(p)-balls in all the cases where the extremisers are known. Our methods are mainly probabilistic, ex-ploring connections between negative moments of projections of random vec-tors uniformly distributed on convex bodies and volume of their sections.
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作者：Cannizzaro, Giuseppe; Haunschmid-Sibitz, Levi; Toninelli, Fabio
作者单位：University of Warwick; Technische Universitat Wien
摘要：The present work is devoted to the study of the large time behaviour of a critical Brownian diffusion in two dimensions, whose drift is divergence-free, ergodic and given by the curl of the 2-dimensional Gaussian free field. We prove the conjecture, made in (J. Stat. Phys. 147 (2012) 113-131), according to which the diffusion coefficient D(t) diverges as root/log t for t ->infinity. Start-ing from the fundamental work by Alder and Wainwright (Phys. Rev. Lett. 18 (1967) 988-990), logarithmicall...
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作者：Sellke, Mark
作者单位：Stanford University
摘要：In the Gilbert-Shannon-Reeds shuffle, a deck of N cards is cut into two approximately equal parts which are riffled together uniformly at random. Bayer and Diaconis (Ann. Appl. Probab. 2 294-313) famously showed that this Markov chain undergoes cutoff in total variation after 3 log(N) 2log(2) shuffles. We establish cutoff for the more general asymmetric riffle shuffles in which one cuts the deck into differently sized parts. The value of the cutoff point confirms a conjecture of Lalley from 20...
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作者：Pete, Gabor; Timar, Adam
作者单位：HUN-REN; HUN-REN Alfred Renyi Institute of Mathematics; University of Iceland
摘要：We prove the rather counterintuitive result that there exist finite transitive graphs H and integers k such that the Free Uniform Spanning Forest in the direct product of the k-regular tree and H has infinitely many trees almost surely. This shows that the number of trees in the FUSF is not a quasi-isometry invariant. Moreover, we give two different Cayley graphs of the same virtu-ally free group such that the FUSF has infinitely many trees in one, but is connected in the other, answering a qu...
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作者：Harris, Simon C.; Horton, Emma; Kyprtanou, Andreas E.; Wang, Minmin
作者单位：University of Auckland; Inria; University of Bath; University of Sussex
摘要：We consider the classical Yaglom limit theorem for a branching Markov process X = (X-t, t >= 0), with nonlocal branching mechanism in the setting that the mean semigroup is critical, that is, its leading eigenvalue is zero. In particular, we show that there exists a constant c(f ) such that Law(< f, X-t >/t < f, X-t > > 0) -> e(c)(f), t -> infinity, where e(c)(f ) is an exponential random variable with rate c(f ) and the con-vergence is in distribution. As part of the proof, we also show that ...
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作者：Miclo, Laurent; Patie, Pierre; Sarkar, Rohan
作者单位：Universite de Toulouse; Universite Toulouse 1 Capitole; Toulouse School of Economics; Cornell University
摘要：The first aim of this paper is to introduce a class of Markov chains on Z(+) which are discrete self-similar in the sense that their semigroups satisfy an in-variance property expressed in terms of a discrete random dilation operator. After showing that this latter property requires the chains to be upward skip-free, we first establish a gateway intertwining relation between the semigroup of such chains and the one of spectrally negative self-similar Markov pro-cesses on R+. As a by-product, w...
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作者：Fitzgerald, Will; Tribe, Roger; Zaboronski, Oleg
作者单位：University of Manchester; University of Warwick
摘要：Motivated by the phenomenon of duality for interacting particle systems, we introduce two classes of Pfaffian kernels describing a number of Pfaf-fian point processes in the bulk and at the edge. Using the probabilistic method due to Mark Kac, we prove two Szego-type asymptotic expansion theorems for the corresponding Fredholm Pfaffians. The idea of the proof is to introduce an effective random walk with transition density determined by the Pfaffian kernel, express the logarithm of the Fredhol...
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作者：Berestycki, Julien; Brunet, Eric; Nolen, James; Penington, Sarah
作者单位：University of Oxford; Universite PSL; Ecole Normale Superieure (ENS); Universite Paris Cite; Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); Duke University; University of Bath
摘要：The Brownian bees model is a branching particle system with spatial selection. It is a system of N particles which move as independent Brownian motions in Rd and independently branch at rate 1, and, crucially, at each branching event, the particle which is the furthest away from the origin is removed to keep the population size constant. In the present work we prove that, as N -> oo, the behaviour of the particle system is well approximated by the solution of a free boundary problem (which is ...
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作者：Bruno, Stefano; Gess, Benjamin; Weber, Hendrik
作者单位：University of Bath; University of Bielefeld
摘要：We prove optimal regularity estimates in Sobolev spaces in time and space for solutions to stochastic porous medium equations. The noise term considered here is multiplicative, white in time and coloured in space. The coefficients are assumed to be Holder continuous, and the cases of smooth coefficients of, at most, linear growth as well as root u are covered by our as-sumptions. The regularity obtained is consistent with the optimal regularity derived for the deterministic porous medium equat...
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作者：Gangbo, Wilfrid; Meszaros, Alpar R.; Mou, Chenchen; Zhang, Jianfeng
作者单位：University of California System; University of California Los Angeles; Durham University; City University of Hong Kong; University of Southern California
摘要：In this manuscript we propose a structural condition on nonseparable Hamiltonians, which we term displacement monotonicity condition, to study second-order mean field games master equations. A rate of dissipation of a bilinear form is brought to bear a global (in time) well-posedness theory, based on a priori uniform Lipschitz estimates on the solution in the measure variable. Displacement monotonicity being sometimes in dichotomy with the widely used Lasry-Lions monotonicity condition, the no...
