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Spanning trees of graphs on surfaces and the intensity of loop-erased random walk on Z^2
Uniform spanning tree loop-erased random walk abelian sandpile model
2011/9/14
Abstract: We show how to compute the probabilities of various connection topologies for uniformly random spanning trees on graphs embedded in surfaces. As an application, we show how to compute the "i...
Moments of random sums and Robbins' problem of optimal stopping
Moments of random sums Robbins' problem Probability
2011/9/13
Abstract: Robbins' problem of optimal stopping asks one to minimise the expected {\it rank} of observation chosen by some nonanticipating stopping rule. We settle a conjecture regarding the {\it value...
The scaling limit of the critical one-dimensional random Schrodinger operator
critical one-dimensional random Schrodinger operator Probability
2011/9/9
Abstract: We consider two models of one-dimensional discrete random Schrodinger operators (H_n \psi)_l ={\psi}_{l-1}+{\psi}_{l +1}+v_l {\psi}_l, {\psi}_0={\psi}_{n+1}=0 in the cases v_k=\sigma {\omega...
Compositions, Random Sums and Continued Random Fractions of Poisson and Fractional Poisson Processes
Fractional birth process Bell polynomials Mittag–Leffler functions Fibonacci numbers continued fractions Poisson random fields
2011/9/8
Abstract: In this paper we consider the relation between random sums and compositions of different processes. In particular, for independent Poisson processes $N_\alpha(t)$, $N_\beta(t)$, $t>0$, we sh...
Branching diffusions in random environment
Branching process random environment diffusion approximation Laplace transform survival probability backbone construction
2011/9/6
Abstract: We consider the diffusion approximation of branching processes in random environment (BPREs). This diffusion approximation is similar to and mathematically more tractable than BPREs. We obta...
Large deviations for truncated heavy-tailed random variables: a boundary case
heavy tails truncation regular variation large deviation
2011/9/6
Abstract: This paper investigates the decay rate of the probability that the row sum of a triangular array of truncated heavy tailed random variables is larger than an integer (k) times the truncating...
Convergence in law for the branching random walk seen from its tip
branching random walk Convergence its tip Probability
2011/9/5
Abstract: Considering a critical branching random walk on the real line. In a recent paper, Aidekon [3] developed a powerful method to obtain the convergence in law of its minimum after a log-factor n...
Fractional relaxation equations and Brownian crossing probabilities of a random boundary
Fractional relaxation equation Generalized Mittag-Leffler functions Processes with random time
2011/9/5
Abstract: We analyze here different forms of fractional relaxation equations of order {\nu}\in(0,1) and we derive their solutions both in analytical and in probabilistic forms. In particular we show t...
A 0-1 law for vertex-reinforced random walks on $\mathbb{Z}$ with weight of order $k^α$, $α<1/2$
vertex-reinforced random Probability
2011/9/5
Abstract: We prove that Vertex Reinforced Random Walk on $\mathbb{Z}$ with weight of order $k^\alpha$, with $\alpha\in [0,1/2)$, is either almost surely recurrent or almost surely transient. This impr...
Effect of truncation on large deviations for heavy-tailed random vectors
heavy tails truncation regular variation large deviation
2011/9/5
Abstract: This paper studies the effect of truncation on the large deviations behavior of the partial sum of a triangular array coming from a truncated power law model. Each row of the triangular arra...
A generalized Isserlis theorem for location mixtures of Gaussian random vectors
Isserlis theorem normal-variance mixture generalized hyperbolic distribution
2011/9/2
Abstract: In a recent paper, Michalowicz et al. provide an extension of Isserlis theorem to the case of a Bernoulli location mixture of a Gaussian vector. We extend here this result to the case of any...
Partial match queries in random quadtrees
random quadtrees Probability Data Structures and Algorithms
2011/9/2
Abstract: We consider the problem of recovering items matching a partially specified pattern in multidimensional trees (quad trees and k-d trees). We assume the traditional model where the data consis...
Schroder's problems and scaling limits of random trees
Schroder's problems Probability scaling limits of random trees
2011/8/31
Abstract: In a classic paper Schr\"oder posed four combinatorial problems about the number of certain types of bracketings of words and sets. Here we address what these bracketings look like on averag...
Abstract: In this paper, we discuss three extrapolation methods for alpha-stable random fields with 1roofs of the existence and uniqueness of the solutions for each...
The Simple Random Walk Snake on Z^4 is Recurrent
Simple Random Walk Snake Recurrent Probability
2011/8/26
Abstract: Consider the branching simple random walk on Z^d indexed by a critical geometric Galton-Watson tree conditioned to survive. Using the concept of unimodular random graphs, we show that the wa...