The Annals of Probability

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• Ulam's problem and Hammersley's process AI翻译
  作者：Groeneboom, P
  作者单位：Delft University of Technology; Vrije Universiteit Amsterdam
  摘要：Let L-n be the length of the longest increasing subsequence of a random permutation of the numbers 1,..., n, for the uniform distribution on the set of permutations. Hammersley's interacting particle process, implicit in Hammersley (1972), has been used in Aldous and Diaconis (1995) to provide a soft hydrodynamical argument for proving that lim(n --> infinity) ELn/rootn = 2. We show in this note that the latter result is in fact an immediate consequence of properties of a random 2-dimensional ...
• Renormalization of the voter model in equilibrium AI翻译
  作者：Zähle, I
  作者单位：University of Erlangen Nuremberg
  摘要：We consider the d-dimensional voter model for d greater than or equal to 3. Our interest is the large scale limit of the equilibrium state of the voter model, where we prove the d = 3 results of [1] for d greater than or equal to 4, which turn out to be of a different nature than for d = 3. For this purpose we use the historical process. We establish some surprising facts about the Green's function of random walks in dimension d > 4, which lead to the different features in d = 3 versus d > 4. ...
• Uniform spanning forests AI翻译
  作者：Benjamini, I; Lyons, R; Peres, Y; Schramm, O
  作者单位：Weizmann Institute of Science; Hebrew University of Jerusalem; Indiana University System; Indiana University Bloomington; University of California System; University of California Berkeley
  摘要：We study uniform spanning forest measures on infinite graphs. which are weak limits of uniform spanning tree measures from finite subgraphs. These limits can be taken with free (FSF) or wired (WSF) boundary conditions. Pemantle proved that the free and wired spanning forests coincide in Z(d) and that they give a single tree iff d less than or equal to 4. In the present work, we extend Pemantle's alternative to general graphs and exhibit further connections of uniform spanning forests to random...
• Kolmogorov's test for the Brownian snake AI翻译
  作者：Delmas, JF; Dhersin, JS
  作者单位：Institut Polytechnique de Paris; Ecole des Ponts ParisTech; Universite Paris Cite
  摘要：We present a Kolmogorov's test for the Brownian snake. This result was conjectured by Le Gall in 1998. It has to be compared with Kolmogorov's test for super Brownian motion by Dhersin and Le Gall.
• Invariant probability distributions for measure-valued diffusions AI翻译
  作者：Pinsky, RG
  作者单位：Technion Israel Institute of Technology
  摘要：We investigate the set of invariant probability distributions for measure-valued diffusion processes corresponding to semilinear operators of the form u(t) = L(0)u+betau-alphau(2), where L-0 = (1/2) Sigma(i)(,j=1)(d) alpha(i,j) alpha(2)/alphax(i)alphax(j) + Sigma(i)(= 1)(d) b(i) alpha/alphax(i).
• A zero-one law for planar random walks in random environment AI翻译
  作者：Zerner, MPW; Merkl, F
  作者单位：Stanford University; University of Bielefeld; Technion Israel Institute of Technology
  摘要：We solve the problem posed by S. A. Kalikow whether the event that the x-coordinate of a random walk in a two-dimensional random environment approaches infinity has necessarily probability either zero or one. The answer is yes if we assume the environment to be i.i.d. and in general no if we allow the environment to be just stationary and ergodic.
• On the distribution of ranked heights of excursions of a Brownian bridge AI翻译
  作者：Pitman, J; Yor, M
  作者单位：University of California System; University of California Berkeley; Sorbonne Universite
  摘要：The distribution of the sequence of ranked maximum and minimum values attained during excursions of a standard Brownian bridge (B-t(br), 0 less than or equal to t less than or equal to 1) is described. The height M-j(br+) of the jth highest maximum over a positive excursion of the bridge has the same distribution as M-1(br+)/j, where the distribution of Mb(1)(br+) = Sup(0 less than or equal tot less than or equal to1)B(t)(br) is given by Levy's formula P(M-1(br+) > x) = e(-2x2). The probabilit...
• Invariance principles with logarithmic averaging for Markov processes AI翻译
  作者：Maaoula, F
  作者单位：Universite de Tunis-El-Manar; Faculte des Sciences de Tunis (FST)
  摘要：We extend the almost-sure central limit theorem to martingale additive functionals of a recurrent Markov process. In the particular case of positive recurrence, we also derive two invariance principles similar to the central limit theorem and the law of the iterated logarithm.
• Markov chains indexed by -N: Existence and behaviour AI翻译
  作者：Brossard, J; Leuridan, C
  作者单位：Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
• Power-law corrections to exponential decay of connectivities and correlations in lattice models AI翻译
  作者：Alexander, KS
  作者单位：University of Southern California
  摘要：Consider a translation-invariant bond percolation model on the integer lattice which has exponential decay of connectivities, that is, the probability of a connection 0 <----> x by a path of open bonds decreases like exp(-m(theta)\x \) for some positive constant m(theta) which may depend on the direction a = x/\x \. In two and three dimensions, it is shown that if the model has an appropriate mixing property and satisfies a special case of the FKG property, then there is at most a power-law co...