Inequality of two critical probabilities for percolation.
Infinite paths and cliques in random graphs
We study the thresholds for the emergence of various properties in random subgraphs of (ℕ, <). In particular, we give sharp sufficient conditions for the existence of (finite or infinite) cliques and paths in a random subgraph. No specific assumption on the probability is made. The main tools are a topological version of Ramsey theory, exchangeability theory and elementary ergodic theory.
Information recovery from randomly mixed-up message text.
Intégration d'une suite récurrente qui se présente dans une question de probabilité
Intersections of randomly embedded sparse graphs are Poisson.
Irreducible compositions and the first return to the origin of a random walk.
Isolated trees in a bichromatic random graph
Isolated trees in a random graph
Jack deformations of Plancherel measures and traceless Gaussian random matrices.
Lattice paths, sampling without replacement, and limiting distributions.
Limit distributions for multitype branching processes of -ary search trees
Let be an integer. The so-called-ary search treeis a discrete time Markov chain which is very popular in theoretical computer science, modelling famous algorithms used in searching and sorting. This random process satisfies a well-known phase transition: when , the asymptotic behavior of the process is Gaussian, but for it is no longer Gaussian and a limit of a complex-valued martingale arises. In this paper, we consider the multitype branching process which is the continuous time version...
Limit shapes of Gibbs distributions on the set of integer partitions : the expansive case
We find limit shapes for a family of multiplicative measures on the set of partitions, induced by exponential generating functions with expansive parameters, ak∼Ckp−1, k→∞, p>0, where C is a positive constant. The measures considered are associated with the generalized Maxwell–Boltzmann models in statistical mechanics, reversible coagulation–fragmentation processes and combinatorial structures, known as assemblies. We prove a central limit theorem for fluctuations of a properly scaled partition...
Limit theorems for the number of maxima in random samples from planar regions.
Limiting behavior for the distance of a random walk.
Local limit approximations for Lagrangian distributions.
Loi de probabilité des écarts
Lois empiriques et distance de Prokhorov
Longest increasing subsequences of random colored permutations.
Markov bases of conditional independence models for permutations
The L-decomposable and the bi-decomposable models are two families of distributions on the set of all permutations of the first positive integers. Both of these models are characterized by collections of conditional independence relations. We first compute a Markov basis for the L-decomposable model, then give partial results about the Markov basis of the bi-decomposable model. Using these Markov bases, we show that not all bi-decomposable distributions can be approximated arbitrarily well by...
Martingales and profile of binary search trees.