The Annals of Probability

最新文章

• PINNING AND WETTING TRANSITION FOR (1+1)-DIMENSIONAL FIELDS WITH LAPLACIAN INTERACTION AI翻译
  作者：Caravenna, Francesco; Deuschel, Jean-Dominique
  作者单位：University of Padua; Technical University of Berlin
  摘要：We consider a random field phi : {1,..., N} -> R as a model fora linear chain attracted to the defect line phi = 0. that is, the x-axis. The free law of the field is specified by the density exp(-Sigma(i) V(Delta phi(i))) with respect to the Lebesgue measure on R(N), where Delta is the discrete Laplacian and we allow for a very large class of potentials V(.). The interaction with the defect line is introduced by giving the field a reward epsilon >= 0 each time it touches the x-axis. We call th...
• Central limit theorems for Gaussian polytopes (vol 35, pg 1593, 2007) AI翻译
  作者：Barany, Imre; Vu, Van
  作者单位：Hungarian Academy of Sciences; HUN-REN; HUN-REN Alfred Renyi Institute of Mathematics; University of London; University College London; Rutgers University System; Rutgers University New Brunswick
• The dimension of the SLE curves AI翻译
  作者：Beffara, Vincent
  作者单位：Ecole Normale Superieure de Lyon (ENS de LYON); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
  摘要：Let gamma be the curve generating a Schramm-Loewner Evolution (SLE) process, with parameter kappa >= 0. We prove that, with probability one, the Hausdorff dimension of gamma is equal to Min(2, 1 + kappa/8).
• Approximate zero-one laws and sharpness of the percolation transition in a class of models including two-dimensional ising percolation AI翻译
  作者：van den Berg, J.
  摘要：One of the most well-known classical results for site percolation on the square lattice is the equation p(c) + p(c)* = 1. In words, this equation means that for all vaues not equal p(c) of the Parameter p. the following holds: either a.s. there is all infinite open cluster or a.s. there is an infinite closed star cluster. This result is closely related to the percolation transition being sharp: below p(c), the size of the open cluster of a given vertex is not only (a.s.) finite. but has a dist...
• The LIL for canonical U-statistics AI翻译
  作者：Adamczak, Radoslaw; Latala, Rafal
  作者单位：Polish Academy of Sciences; Institute of Mathematics of the Polish Academy of Sciences; University of Warsaw
  摘要：We give necessary and sufficient conditions for the (bounded) law of the iterated logarithm for canonical U-statistics of arbitrary order d, extending the previously known results for d = 2. The nasc's are expressed as growth conditions on a parameterized family of norms associated with the U-statistics kernel.
• Decay of correlations in nearest-neighbor self-avoiding walk, percolation, lattice trees and animals AI翻译
  作者：Hara, Takashi
  作者单位：Kyushu University
  摘要：We consider nearest-neighbor self-avoiding walk, bond percolation, lattice trees, and bond lattice animals on Z(d). The two-point functions of these models are respectively the generating function for self-avoiding walks from the origin to x epsilon Z(d), the probability of a connection from the origin to x, and the generating functions for lattice trees or lattice animals containing the origin and x. Using the lace expansion, we prove that the two-point function at the critical point is asymp...
• A note on multitype branching processes with immigration in a random environment AI翻译
  作者：Roitershtein, Alexander
  作者单位：University of British Columbia
  摘要：We consider a multitype branching process with immigration in a random environment introduced by Key in [Ann. Probab. 15 (1987) 344-353]. It was shown by Key that, under the assumptions made in [Ann. Probab. 15 (1987) 344-353], the branching process is subcritical in the sense that it converges to a proper limit law. We complement this result by a strong law of large numbers and a central limit theorem for the partial sums of the process. In addition, we study the asymptotic behavior of oscill...
• On the paper weak convergence of some classes of martingales with jumps AI翻译
  作者：Nishiyama, Yoichi
  作者单位：Research Organization of Information & Systems (ROIS); Institute of Statistical Mathematics (ISM) - Japan
  摘要：This note extends some results of Nishiyama [Ann. Probab. 28 (2000) 685-712]. A maximal inequality for stochastic integrals with respect to integer-valued random measures which may have infinitely many jumps on compact time intervals is given. By using it, a tightness criterion is obtained; if the so-called quadratic modulus is bounded in probability and if a certain entropy condition on the parameter space is satisfied, then the tightness follows. Our approach is based on the entropy techniqu...
• Conditioned square functions for noncommutative martingales AI翻译
  作者：Randrianantoanina, Narcisse
  作者单位：University System of Ohio; Miami University
  摘要：We prove a weak-type (1, 1) inequality involving conditioned versions of square functions for martingales in noncommutative L-P-spaces associated with finite von Neumann algebras. As application, we determine the optimal orders for the best constants in the noncommutative Burkholder/Rosenthal inequalities from [Ann. Probab. 31 (2003) 948-995]. We also discuss BMO-norms of sums of noncommuting order-independent operators.
• Harnack inequality and applications for stochastic generalized porous media equations AI翻译
  作者：Wang, Feng-Yu
  作者单位：Beijing Normal University
  摘要：By using coupling and Girsanov transformations, the dimension-free Harnack inequality and the strong Feller property are proved for transition semigroups of solutions to a class of stochastic generalized porous media equations. As applications, explicit upper bounds of the L-P-norm of the density as well as hypercontractivity, ultracontractivity and compactness of the corresponding semigroup are derived.