3-4期

最新文章

• Imaginary geometry I: interacting SLEs AI翻译
  作者：Miller, Jason; Sheffield, Scott
  作者单位：Microsoft; Massachusetts Institute of Technology (MIT); University of Cambridge
  摘要：Fix constants and , and let h be an instance of the Gaussian free field on a planar domain. We study flow lines of the vector field starting at a fixed boundary point of the domain. Letting vary, one obtains a family of curves that look locally like processes with (where ), which we interpret as the rays of a random geometry with purely imaginary curvature. We extend the fundamental existence and uniqueness results about these paths to the case that the paths intersect the boundary. We also sh...
• Quenched invariance principle for simple random walk on clusters in correlated percolation models AI翻译
  作者：Procaccia, Eviatar B.; Rosenthal, Ron; Sapozhnikov, Artem
  作者单位：University of California System; University of California Los Angeles; Swiss Federal Institutes of Technology Domain; ETH Zurich
  摘要：We prove a quenched invariance principle for simple random walk on the unique infinite percolation cluster for a general class of percolation models on , , with long-range correlations introduced in (Drewitz et al. in J Math Phys 55(8):083307, 2014), solving one of the open problems from there. This gives new results for random interlacements in dimension at every level, as well as for the vacant set of random interlacements and the level sets of the Gaussian free field in the regime of the so...
• The phase transitions of the planar random-cluster and Potts models with are sharp AI翻译
  作者：Duminil-Copin, Hugo; Manolescu, Ioan
  作者单位：University of Geneva
  摘要：We prove that random-cluster models with on a variety of planar lattices have a sharp phase transition, that is that there exists some parameter below which the model exhibits exponential decay and above which there exists a.s. an infinite cluster. The result may be extended to the Potts model via the Edwards-Sokal coupling. Our method is based on sharp threshold techniques and certain symmetries of the lattice; in particular it makes no use of self-duality. Part of the argument is not restric...
• Affine Lie algebras and conditioned space-time Brownian motions in affine Weyl chambers AI翻译
  作者：Defosseux, Manon
  作者单位：Universite Paris Cite
  摘要：We construct a sequence of Markov processes on the set of dominant weights of an affine Lie algebra g considering tensor product of irreducible highest weight modules of g and specializations of the characters involving the Weyl vector.. We show that it converges towards a space-time Brownian motion with a drift, conditioned to remain in a Weyl chamber associated to the root system of g. This extends in particular the results of Defosseux (arXiv:1401.3115,2014) to any affine Lie algebras, in t...
• Normal approximation on Poisson spaces: Mehler's formula, second order Poincar, inequalities and stabilization AI翻译
  作者：Last, Guenter; Peccati, Giovanni; Schulte, Matthias
  作者单位：Helmholtz Association; Karlsruhe Institute of Technology; University of Luxembourg
  摘要：We prove a new class of inequalities, yielding bounds for the normal approximation in the Wasserstein and the Kolmogorov distance of functionals of a general Poisson process (Poisson random measure). Our approach is based on an iteration of the classical Poincar, inequality, as well as on the use of Malliavin operators, of Stein's method, and of an (integrated) Mehler's formula, providing a representation of the Ornstein-Uhlenbeck semigroup in terms of thinned Poisson processes. Our estimates ...
• Harnack inequalities on weighted graphs and some applications to the random conductance model AI翻译
  作者：Andres, Sebastian; Deuschel, Jean-Dominique; Slowik, Martin
  作者单位：University of Bonn; Technical University of Berlin
  摘要：We establish elliptic and parabolic Harnack inequalities on graphs with unbounded weights. As an application we prove a local limit theorem for a continuous time random walk in an environment of ergodic random conductances taking values in satisfying some moment conditions.
• Optimal eigen expansions and uniform bounds AI翻译
  作者：Jirak, Moritz
  作者单位：Humboldt University of Berlin
  摘要：Let be a stationary process with associated lag operators . Uniform asymptotic expansions of the corresponding empirical eigenvalues and eigenfunctions are established under almost optimal conditions on the lag operators in terms of the eigenvalues (spectral gap). In addition, the underlying dependence assumptions are optimal in a certain sense, including both short and long memory processes. This allows us to study the relative maximum deviation of the empirical eigenvalues under very general...
• Absolute continuity and singularity of Palm measures of the Ginibre point process AI翻译
  作者：Osada, Hirofumi; Shirai, Tomoyuki
  作者单位：Kyushu University; Kyushu University
  摘要：We prove a dichotomy between absolute continuity and singularity of the Ginibre point process and its reduced Palm measures , namely, reduced Palm measures and for and are mutually absolutely continuous if and only if ; they are singular each other if and only if . Furthermore, we give an explicit expression of the Radon-Nikodym density for dG(x)/dG(y) for x, y is an element of C-l.
• Random walks with different directions AI翻译
  作者：Herdade, Simo; Vu, Van
  作者单位：Rutgers University System; Rutgers University New Brunswick; Yale University
  摘要：As an extension of Polya's classical result on random walks on the square grids (), we consider a random walk where the steps, while still have unit length, point to different directions. We show that in dimensions at least 4, the returning probability after n steps is at most , which is sharp. The real surprise is in dimensions 2 and 3. In dimension 2, where the traditional grid walk is recurrent, our upper bound is , which is much worse than in higher dimensions. In dimension 3, we prove an ...