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 lower bound in the law of the iterated logarithm for general lacunary series
We prove a lower bound in a law of the iterated logarithm for sums of the form where f satisfies certain conditions and the satisfy the Hadamard gap condition .
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 martingale proof of the Khinchin iterated logarithm law for Wiener processes
A minimum entropy problem for stationary reversible stochastic spin systems on the infinite lattice
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 Multiparameter Strongly Superadditive Ergodic Theorem.
A multiparameter variant of the Salem-Zygmund central limit theorem on lacunary trigonometric series
We prove the central limit theorem for the multisequence where , are reals, are partially hyperbolic commuting s × s matrices, and x is a uniformly distributed random variable in . The main tool is the S-unit theorem.
A Nearly Degenerate Random Variable Occurring in an Occupancy Problem.
A new large deviation inequality for -statistics of order
A new large deviation inequality for U-statistics of order 2
We prove a new large deviation inequality with applications when projecting a density on a wavelet basis.
A new semigroup technique in Poisson approximation.
A non-ballistic law of large numbers for random walks in i. i. d. random environment.
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,...