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作者：Hammer, Matthias; Ortgiese, Marcel; Vollering, Florian
作者单位：Technical University of Berlin; University of Bath
摘要：The symbiotic branching model is a spatial population model describing the dynamics of two interacting types that can only branch if both types are present. A classical result for the underlying stochastic partial differential equation identifies moments of the solution via a duality to a system of Brownian motions with dynamically changing colors. In this paper, we revisit this duality and give it a new interpretation. This new approach allows us to extend the duality to the limit as the bran...
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作者：Beffara, Vincent; Chhita, Sunil; Johansson, Kurt
作者单位：Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); Centre National de la Recherche Scientifique (CNRS); Durham University; Royal Institute of Technology
摘要：Domino tilings of the two-periodic Aztec diamond feature all of the three possible types of phases of random tiling models. These phases are determined by the decay of correlations between dominoes and are generally known as solid, liquid and gas. The liquid-solid boundary is easy to define microscopically and is known in many models to be described by the Airy process in the limit of a large random tiling. The liquid-gas boundary has no obvious microscopic description. Using the height functi...
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作者：Do, Yen; Oanh Nguyen; Vu, Van
作者单位：University of Virginia; Yale University; Yale University; National University of Singapore
摘要：In this paper, we prove optimal local universality for roots of random polynomials with arbitrary coefficients of polynomial growth. As an application, we derive, for the first time, sharp estimates for the number of real roots of these polynomials, even when the coefficients are not explicit. Our results also hold for series; in particular, we prove local universality for random hyperbolic series.
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作者：Catellier, Remi; Chouk, Khalil
作者单位：Universite PSL; Universite Paris-Dauphine; Universite Cote d'Azur; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Technical University of Berlin; Centre National de la Recherche Scientifique (CNRS); Universite Cote d'Azur; Technical University of Berlin
摘要：We prove the existence and uniqueness of a local in time solution to the periodic Phi(4)(3) model of stochastic quantisation using the method of paracontrolled distributions introduced recently by M. Gubinelli, P. Imkeller and N. Perkowski in [Forum Math., Pi 3 (2015) e6].
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作者：Sarkar, Sourav; Roy, Parthanil
作者单位：University of California System; University of California Berkeley; Indian Statistical Institute; Indian Statistical Institute Bangalore
摘要：In this work, we investigate the extremal behaviour of left-stationary symmetric alpha-stable (S alpha S) random fields indexed by finitely generated free groups. We begin by studying the rate of growth of a sequence of partial maxima obtained by varying the indexing parameter of the field over balls of increasing size. This leads to a phase-transition that depends on the ergodic properties of the underlying nonsingular action of the free group but is different from what happens in the case of...
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作者：Le Page, E.; Peigne, M.; Pham, C.
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We study the asymptotic behaviour of the probability of non-extinction of a critical multi-type Galton-Watson process in i.i.d. random environments by using limit theorems for products of positive random matrices. Under suitable assumptions, the survival probability is proportional to 1/root n.
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作者：Rembart, Franz; Winkel, Matthias
作者单位：University of Oxford
摘要：We introduce a general recursive method to construct continuum random trees (CRTs) from independent copies of a random string of beads, that is, any random interval equipped with a random discrete probability measure, and from related structures. We prove the existence of these CRTs as a new application of the fixpoint method for recursive distribution equations formalised in high generality by Aldous and Bandyopadhyay. We apply this recursive method to show the convergence to CRTs of various ...
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作者：Gess, Benjamin; Hofmanova, Martina
作者单位：Max Planck Society; University of Bielefeld; Technical University of Berlin
摘要：We study quasilinear degenerate parabolic-hyperbolic stochastic partial differential equations with general multiplicative noise within the framework of kinetic solutions. Our results are twofold: First, we establish new regularity results based on averaging techniques. Second, we prove the existence and uniqueness of solutions in a full L-1 setting requiring no growth assumptions on the nonlinearities. In addition, we prove a comparison result and an L-1 -contraction property for the solution...
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作者：Tarrago, Pierre
作者单位：CIMAT - Centro de Investigacion en Matematicas
摘要：We investigate the asymptotic behavior of random paths on a graded graph which describes the subword order for words in two letters. This graph, denoted by Z, has been introduced by Viennot, who also discovered a remarkable bijection between paths on Z. and sequences of permutations. Later on, Gnedin and Olshanski used this bijection to describe the set of Gibbs measures on this graph. Both authors also conjectured that the Martin boundary of Z. should coincide with its minimal boundary. We gi...
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作者：Wu, Hao
作者单位：Tsinghua University
摘要：We derive the alternating arm exponents of the critical Ising model. We obtain six different patterns of alternating boundary arm exponents which correspond to the boundary conditions (circle minus circle plus), (circle minus free) and (free free), and the alternating interior arm exponents.
