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作者：Cabezas, M.; Rolla, L. T.; Sidoravicius, V.
作者单位：Instituto Nacional de Matematica Pura e Aplicada (IMPA); Pontificia Universidad Catolica de Chile; University of Buenos Aires; New York University; NYU Shanghai; New York University
摘要：We study an infinite system of moving particles, where each particle is of type A or B. Particles perform independent random walks at rates D-A > 0 and D-B >= 0, and the interaction is given by mutual annihilation A + B -> empty set. The initial condition is i.i.d. with finite first moment. We show that this system is site-recurrent, that is, each site is visited infinitely many times. We also generalize a lower bound on the density decay of Bramson and Lebowitz by considering a construction t...
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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：Richier, Loic
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique
摘要：We discuss asymptotics for the boundary of critical Boltzmann planar maps under the assumption that the distribution of the degree of a typical face is in the domain of attraction of a stable distribution with parameter it has a component homeomorphic to the half-plane. As an application, we identify the limits of loops conditioned to be large in the rigid loop model on quadrangulations, proving thereby a conjecture of Curien and Kortchemski.
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作者：Panagiotou, Konstantinos; Stufler, Benedikt
作者单位：University of Munich; Ecole Normale Superieure de Lyon (ENS de LYON)
摘要：Polya trees are rooted trees considered up to symmetry. We establish the convergence of large uniform random Polya trees with arbitrary degree restrictions to Aldous' Continuum Random Tree with respect to the Gromov-Hausdorff metric. Our proof is short and elementary, and it is based on a novel decomposition: it shows that the global shape of a random Polya tree is essentially dictated by a large Galton-Watson tree that it contains. We also derive sub-Gaussian tail bounds for both the height a...
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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...
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作者：Lupu, Titus; Werner, Wendelin
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We further investigate properties of the Gaussian free field (GFF) on the metric graph associated to a discrete weighted graph (where the edges of the latter are replaced by continuous line-segments of appropriate length) that has been introduced by the first author. On such a metric graph, the GFF is a random continuous function that generalises one-dimensional Brownian bridges so that one-dimensional techniques can be used. In the present paper, we define and study the pseudo-metric defined ...
