A Hölderian FCLT for some multiparameter summation process of independent non-identically distributed random variables.
A law of the iterated logarithm for the sample covariance matrix.
A limit law for the root value of minimax trees.
A limit theorem for functionals of a Poisson process
A limit theorem for joint distribution of order-statistics from stationary Gaussian sequences
A limit theorem for the position of a particle in the Lorentz model.
A limit theorem for the q-convolution
The q-convolution is a measure-preserving transformation which originates from non-commutative probability, but can also be treated as a one-parameter deformation of the classical convolution. We show that its commutative aspect is further certified by the fact that the q-convolution satisfies all of the conditions of the generalized convolution (in the sense of Urbanik). The last condition of Urbanik's definition, the law of large numbers, is the crucial part to be proved and the non-commutative...
A Local Limit Theorem for Attraction to the Standard Normal Law: The Case of Infinitive Variance.
A local limit theorem for directed polymers in random media : the continuous and the discrete case
A local limit theorem for the critical random graph.
A local limit theorem on the semi-direct product of and
A local limit theorem with speed of convergence for euclidean algorithms and diophantine costs
For large N, we consider the ordinary continued fraction of x=p/q with 1≤p≤q≤N, or, equivalently, Euclid’s gcd algorithm for two integers 1≤p≤q≤N, putting the uniform distribution on the set of p and qs. We study the distribution of the total cost of execution of the algorithm for an additive cost function c on the set ℤ+* of possible digits, asymptotically for N→∞. If c is nonlattice and satisfies mild growth conditions, the local limit theorem was proved previously by the second named author....
A log-scale limit theorem for one-dimensional random walks in random environments.
A Markov process underlying the generalized Syracuse algorithm
A martingale central limit theorem
A martingale proof of Dobrushin's theorem for non-homogeneous Markov chains.
A mixed quantum-classical central limit theorem
A randomized q-central or q-commutative limit theorem on a family of bialgebras with one complex parameter is shown.
A new semigroup technique in Poisson approximation.
A non-commutative central limit theorem.
A noncommutative limit theorem for homogeneous correlations
We state and prove a noncommutative limit theorem for correlations which are homogeneous with respect to order-preserving injections. The most interesting examples of central limit theorems in quantum probability (for commuting, anticommuting, and free independence and also various q-qclt's), as well as the limit theorems for the Poisson law and the free Poisson law are special cases of the theorem. In particular, the theorem contains the q-central limit theorem for non-identically distributed variables,...