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作者：Subag, Eliran
作者单位：Weizmann Institute of Science
摘要：In a companion paper we developed the generalized TAP approach for general multispecies spherical mixed p-spin models. In this paper we use it to compute the limit of the free energy at any temperature for all pure mul-tispecies spherical p-spin models, assuming that certain free energies con-verge. Importantly, the pure multispecies models do not satisfy the convexity assumption on the mixture which was crucial in the recent proofs of the Parisi formula for the multispecies Sherrington-Kirkpa...
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作者：Dumaz, Laure; Labbe, Cyril
作者单位：Universite PSL; Ecole Normale Superieure (ENS); Centre National de la Recherche Scientifique (CNRS); Universite Paris Cite; Universite Paris Cite
摘要：We introduce a random differential operator that we call CS tau operator, whose spectrum is given by the Sch(tau) point process introduced by Kritchevski, Valko and Virag (Comm. Math Phys. (2012) 314 775-806) and whose eigen-vectors match with the description provided by Rifkind and Virag (Geom. Funct. Anal. (2018) 28 1394-1419). This operator acts on R-2-valued func-tions from the interval [0, 1] and takes the form [GRAPHICS] . where dB, dW(1) and dW(2) are independent white noises. Then we i...
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作者：Cordero-Erausquin, Dario; Rotem, Liran
作者单位：Sorbonne Universite; Universite Paris Cite; Technion Israel Institute of Technology
摘要：We prove that the (B) conjecture and the Gardner-Zvavitch conjecture are true for all log-concave measures that are rotationally invariant, extend-ing previous results known for Gaussian measures. Actually, our result apply beyond the case of log-concave measures, for instance, to Cauchy measures as well. For the proof, new sharp weighted Poincare inequalities are obtained for even probability measures that are log-concave with respect to a rotation-ally invariant measure.
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作者：Dereudre, David; Vasseur, Thibaut
作者单位：Universite de Lille; Universite Paris Cite
摘要：For an inverse temperature /3 > 0, we define the /3-circular Riesz gas on Rd as any microscopic thermodynamic limit of Gibbs particle systems on the torus interacting via the Riesz potential g(x) = IlxII-s. We focus on the nonintegrable case d -1 < s < d. Our main result ensures, for any dimension d > 1 and inverse temperature /3 > 0, the existence of a /3-circular Riesz gas which is not number-rigid. Recall that a point process is said number rigid if the number of points in a bounded Borel s...
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作者：Chelkak, Dmitry; Izyurov, Konstantin; Mahfouf, Remy
作者单位：Universite PSL; Ecole Normale Superieure (ENS); Russian Academy of Sciences; Steklov Mathematical Institute of the Russian Academy of Sciences; University of Helsinki
摘要：We prove universality of spin correlations in the scaling limit of the planar Ising model on isoradial graphs with uniformly bounded angles and Z-invariant weights. Specifically, we show that in the massive scaling limit, that is, as the mesh size tends to zero at the same rate as the Baxter elliptic parameter tends to 1, the two-point spin correlations in the full plane converge to a universal rotationally invariant limit. These results, together with techniques developed to obtain them, are ...
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作者：Landon, Benjamin; Noack, Christian; Sosoe, Philippe
作者单位：University of Toronto; Purdue University System; Purdue University; Cornell University
摘要：We consider systems of N diffusions in equilibrium interacting through a potential V. We study a height function, which, for the special choice V (x) = e(-x), coincides with the partition function of a stationary semidis-crete polymer, also known as the (stationary) O'Connell-Yor polymer. For a general class of smooth convex potentials (generalizing the O'Connell-Yor case), we obtain the order of fluctuations of the height function by proving matching upper , lower bounds for the variance of o...
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作者：Janson, Svante; Louf, Baptiste
作者单位：Uppsala University
摘要：We study uniformly random maps with a single face, genus g, and size n, as n, g -infinity with g = o(n), in continuation of several previous works on the geometric properties of high genus maps. We calculate the number of short simple cycles, and we show convergence of their lengths (after a well-chosen rescaling of the graph distance) to a Poisson process, which happens to be exactly the same as the limit law obtained by Mirzakhani and Petri (Comment. Math. Helv. 94 (2019) 869-889) when they ...
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作者：Jaramillo, Arturo; Nourdin, Ivan; Nualart, David; Peccati, Giovanni
作者单位：CIMAT - Centro de Investigacion en Matematicas; University of Luxembourg; University of Kansas
摘要：We investigate first and second order fluctuations of additive functionals of a fractional Brownian motion (fBm) of the form [GRAPHICS] . where B={B-t; t >= 0} is a fBm with Hurst parameter H is an element of(0,1), f is a suitable test function and lambda is an element of R. We develop our study by distinguishing two regimes which exhibit different behaviors. When H is an element of(0,1/3), we show that a suitable renormalization of (0.1), compensated by a multiple of the local time of B, conv...
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作者：Lyons, Russell; White, Graham
作者单位：Indiana University System; Indiana University Bloomington
摘要：Consider continuous-time random walks on Cayley graphs where the rate assigned to each edge depends only on the corresponding generator. We show that the limiting speed is monotone increasing in the rates for infinite Cay-ley graphs that arise from Coxeter systems but not for all Cayley graphs. On finite Cayley graphs, we show that the distance-in various senses-to stationarity is monotone decreasing in the rates for Coxeter systems and for abelian groups but not for all Cayley graphs. We also...
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作者：Das, Sayan; Ghosal, Promit
作者单位：Columbia University; Massachusetts Institute of Technology (MIT)
摘要：We consider the Cole-Hopf solution of the (1 + 1)-dimensional KPZ equation started from the narrow wedge initial condition. In this article we ask how the peaks and valleys of the KPZ height function (centered by time/24) at any spatial point grow as time increases. Our first main result is about the law of iterated logarithms for the KPZ equation. As time variable t goes to infinity, we show that the limsup of the KPZ height function with the scaling by root t1/3(loglogt)2/3 is almost surely ...
