-
作者：Herr, Sebastian; Roeckner, Michael; Spitz, Martin; Zhang, Deng
作者单位：University of Bielefeld; Shanghai Jiao Tong University
摘要：We study the three-dimensional stochastic Zakharov system in the energy space, where the Schr & ouml;dinger equation is driven by linear multiplicative noise and the wave equation is driven by additive noise. We prove the well-posedness of the system up to the maximal existence time and provide a blow-up alternative. We further show that the solution exists at least as long as it remains below the ground state. Two main ingredients of our proof are refined rescaling transformations and the nor...
-
作者：Adhikari, Arka; Cao, Sky
作者单位：Stanford University; Massachusetts Institute of Technology (MIT)
摘要：In the setting of lattice gauge theories with finite (possibly non-Abelian) gauge groups at weak coupling, we prove exponential decay of correlations for a wide class of gauge invariant functions, which in particular includes arbitrary functions of Wilson loop observables.
-
作者：Bresar, Miha; Mijatovic, Aleksandar; Wade, Andrew
作者单位：University of Warwick; Durham University
摘要：We quantify the asymptotic behaviour of multidimensional drifltess diffusions in domains unbounded in a single direction with asymptotically normal reflections from the boundary. We identify the critical growth/contraction rates of the domain that separate stability, null recurrence and transience. In the stable case, we prove existence and uniqueness of the invariant distribution and establish the polynomial rate of decay of its tail. We also establish matching polynomial upper and lower boun...
-
作者：Kim, Seonwoo; Seo, Insuk
作者单位：Korea Institute for Advanced Study (KIAS); Seoul National University (SNU); Seoul National University (SNU)
摘要：The main contribution of the current study is two-fold. First, we investigate the energy landscape of the Ising and Potts models on finite twodimensional lattices without external fields in the low-temperature regime. The complete analysis of the energy landscape of these models was unknown because of its complicated plateau saddle structure between the ground states. We characterize this structure completely in terms of a random walk on the set of subtrees of a ladder graph. Second, we provid...
-
作者：Dembin, Barbara; Elboim, Dor; Peled, Ron
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich; Institute for Advanced Study - USA; Tel Aviv University
摘要：We study first-passage percolation on Z(d), d >= 2, with independent weights whose common distribution is compactly supported in (0,infinity) with a uniformly-positive density. Given & varepsilon;>0 and v is an element of Z(d), which edges have probability at least & varepsilon; to lie on the geodesic between the origin and v? It is expected that all such edges lie at distance at most some r(& varepsilon;)r(& varepsilon;) from either the origin or v, but this remains open in dimensions d >= 3....
-
作者：Borga, Jacopo; Boutillier, Cedric; Feray, Valentin; Meliot, Pierre-Loic
作者单位：Stanford University; Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); Universite de Lorraine; Universite Paris Saclay
摘要：We obtain scaling and local limit results for large random Young tableaux of fixed shape )0 via the asymptotic analysis of a determinantal point process due to Gorin and Rahman (2019). More precisely, we prove: - an explicit description of the limiting surface of a uniform random Young tableau of shape )0, based on solving a complex-valued polynomial equation, - a simple criteria to determine if the limiting surface is continuous in the whole domain, - and a local limit result in the bulk of a...
-
作者：Liu, Mingchang; Peltola, Eveliina; Wu, Hao
作者单位：Royal Institute of Technology; University of Bonn; Tsinghua University
摘要：We find explicit SLE(8) partition functions for the scaling limits of Peano curves in the uniform spanning tree (UST) in topological polygons with general boundary conditions. They are given in terms of Coulomb gas integral formulas, which can also be expressed in terms of determinants involving a-periods of a hyperelliptic Riemann surface. We also identify the crossing probabilities for the UST Peano curves as ratios of these partition functions. The partition functions are interpreted as cor...
-
作者：Ang, Morris; Sun, Xin; Yu, Pu; Zhuang, Zijie
作者单位：University of California System; University of California San Diego; Peking University; Massachusetts Institute of Technology (MIT); University of Pennsylvania
摘要：The conformal loop ensemble (CLE) has two phases: for kappa E (8/3, 4], the loops are simple and do not touch each other or the boundary; for kappa E (4, 8), the loops are nonsimple and may touch each other and the boundary. For kappa E (4, 8), we derive the probability that the loop surrounding a given point touches the domain boundary. We also obtain the law of the conformal radius of this loop seen from the given point conditioned on the loop touching the boundary or not, refining a result ...
-
作者：Cerny, Jiri; Drewitz, Alexander; Oswald, Pascal
作者单位：University of Basel; University of Cologne
摘要：We consider one-dimensional branching Brownian motion in a spatially random branching environment (BBMRE) and show that for almost every realisation of the environment, the distributions of the maximal particle of the BBMRE recentred around its median are tight as time evolves. This result is in stark contrast to the fact that the transition fronts in the solution to the randomised Fisher-Kolmogorov-Petrovskii-Piskunov (F-KPP) equation are, in general, not bounded uniformly in time. In particu...
-
作者：Bhamidi, Shankar; Dhara, Souvik; van der Hofstad, Remco
作者单位：University of North Carolina; University of North Carolina Chapel Hill; Purdue University System; Purdue University; Eindhoven University of Technology
摘要：We study the critical behavior for percolation on inhomogeneous random networks on n vertices, where the weights of the vertices follow a power-law distribution with exponent tau is an element of (2, 3). Such networks, often referred to as scale-free networks, exhibit critical behavior when the percolation probability tends to zero at an appropriate rate, as n -> infinity. We identify the critical window for several scale-free random graph models, such as the Norros-Reittu model, Chung-Lu mode...
