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作者：Chen, Wei-Kuo; Handschy, Madeline; Lerman, Gilad
作者单位：University of Minnesota System; University of Minnesota Twin Cities
摘要：We investigate the energy landscape of the mixed even p-spin model with Ising spin configurations. We show that for any given energy level between zero and the maximal energy, with overwhelming probability there exist exponentially many distinct spin configurations such that their energies stay near this energy level. Furthermore, their magnetizations and overlaps are concentrated around some fixed constants. In particular, at the level of maximal energy, we prove that the Hamiltonian exhibits...
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作者：Ahlberg, Daniel; Tassion, Vincent; Teixeira, Augusto
作者单位：Uppsala University; University of Geneva
摘要：We study the phase transition of random radii Poisson Boolean percolation: Around each point of a planar Poisson point process, we draw a disc of random radius, independently for each point. The behavior of this process is well understood when the radii are uniformly bounded from above. In this article, we investigate this process for unbounded (and possibly heavy tailed) radii distributions. Under mild assumptions on the radius distribution, we show that both the vacant and occupied sets unde...
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作者：Bufetov, Alexander I.; Fan, Shilei; Qiu, Yanqi
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Aix-Marseille Universite; Russian Academy of Sciences; Steklov Mathematical Institute of the Russian Academy of Sciences; Kharkevich Institute for Information Transmission Problems of the RAS; HSE University (National Research University Higher School of Economics); Saint Petersburg State University; Central China Normal University; Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Centre National de la Recherche Scientifique (CNRS); Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS
摘要：For a determinantal point process induced by the reproducing kernel of the weighted Bergman space A2(U,.) over a domain U. Cd, we establish the mutual absolute continuity of reduced Palm measures of any order provided that the domain U contains a non-constant bounded holomorphic function. The result holds in all dimensions. The argument uses the H 8 (U)-module structure of A2(U,.). A corollary is the quasi-invariance of our determinantal point process under the natural action of the group of c...
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作者：Conforti, Giovanni; Von Renesse, Max
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; ENSTA Paris; Leipzig University
摘要：In this paper we establish quantitative results about the bridges of the Langevin dynamics and the associated reciprocal processes. They include an equivalence between gradient estimates for bridge semigroups and couplings, comparison principles, bounds of the distance between bridges of different Langevin dynamics, and a logarithmic Sobolev inequality for bridge measures. The existence of an invariant measure for the bridges is also discussed and quantitative bounds for the convergence to the...
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作者：El Karoui, Noureddine
作者单位：University of California System; University of California Berkeley
摘要：We study ridge-regularized generalized robust regression estimators, i.e. in the situation where p/n tends to a finite non-zero limit. Our study here focuses on the situation where the errors 's are heavy-tailed and 's have an elliptical-like distribution. Our assumptions are quite general and we do not require homoskedasticity of 's for instance. We obtain a characterization of the limit of , as well as several other results, including central limit theorems for the entries of (beta) over cap.
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作者：Ioffe, Dmitry; Velenik, Yvan; Wachtel, Vitali
作者单位：Technion Israel Institute of Technology; University of Geneva; University of Augsburg
摘要：We consider families of non-colliding random walks above a hard wall, which are subject to a self-potential of tilted area type. We view such ensembles as effective models for the level lines of a class of -dimensional discrete-height random surfaces in statistical mechanics. We prove that, under rather general assumptions on the step distribution and on the self-potential, such walks converge, under appropriate rescaling, to non-intersecting Ferrari-Spohn diffusions associated with limiting S...
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作者：Bacry, Emmanuel; Gaiffas, Stephane; Muzy, Jean-Francois
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; ENSTA Paris; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Institut Polytechnique de Paris; Ecole Polytechnique; Centre National de la Recherche Scientifique (CNRS); CNRS - Institute for Engineering & Systems Sciences (INSIS)
摘要：This paper gives new concentration inequalities for the spectral norm of a wide class of matrix martingales in continuous time. These results extend previously established Freedman and Bernstein inequalities for series of random matrices to the class of continuous time processes. Our analysis relies on a new supermartingale property of the trace exponential proved within the framework of stochastic calculus. We provide also several examples that illustrate the fact that our results allow us to...
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作者：Bhamidi, Shankar; van der Hofstad, Remco; Sen, Sanchayan
作者单位：University of North Carolina; University of North Carolina Chapel Hill; Eindhoven University of Technology; McGill University
摘要：One major open conjecture in the area of critical random graphs, formulated by statistical physicists, and supported by a large amount of numerical evidence over the last decade (Braunstein et al. in Phys Rev Lett 91(16):168701, 2003; Wu et al. in Phys Rev Lett 96(14):148702, 2006; Braunstein et al. Int J Bifurc Chaos 17(07):2215-2255, 2007; Chen et al. in Phys Rev Lett 96(6):068702, 2006) is as follows: for a wide array of random graph models with degree exponent , distances between typical p...
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作者：Swart, Jan M.
作者单位：Czech Academy of Sciences; Institute of Information Theory & Automation of the Czech Academy of Sciences
摘要：This paper gives a new, simple proof of the known fact that for contact processes on general lattices, in the subcritical regime the expected number of infected sites decays exponentially fast as time tends to infinity. The proof also yields an explicit bound on the survival probability below the critical recovery rate, which shows that the critical exponent associated with this function is bounded from below by its mean-field value. The main idea of the proof is that if the expected number of...
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作者：Borodin, Alexei; Petrov, Leonid
作者单位：Massachusetts Institute of Technology (MIT); Kharkevich Institute for Information Transmission Problems of the RAS; University of Virginia
摘要：We introduce and study the inhomogeneous exponential jump modelan integrable stochastic interacting particle system on the continuous half line evolving in continuous time. An important feature of the system is the presence of arbitrary spatial inhomogeneity on the half line which does not break the integrability. We completely characterize the macroscopic limit shape and asymptotic fluctuations of the height function (=integrated current) in the model. In particular, we explain how the presen...
