Abstract Let $\mu $ be a probability measure on $\mathrm {GL}_d(\mathbb {R})$ , and denote by $S_n:= g_n \cdots g_1$ the associated random matrix product, where $g_j$ are i.i.d. with law . Under assumptions that has finite exponential moment generates proximal strongly irreducible semigroup, we prove Berry–Esseen bound optimal rate $O(1/\sqrt n)$ for coefficients of $S_n$ settling long-standing...

Abstract We prove a quenched local central limit theorem for continuous-time random walks in $${\mathbb {Z}}^d, d\ge 2$$ Z d , ≥ 2 , uniformly-elliptic time-dependent balanced environment which is...

Using Fourier analysis, we study local limit theorems in weak-convergence problems. Among many applications, we discuss random matrix theory, some probabilistic models in number theory, the winding number of complex brownian motion and the classical situation of the central limit theorem, and a conjecture concerning the distribution of values of the Riemann zeta function on the critical line.

By using a generating function approach it is shown that certain functionals of digitial expansion (related to speciic nite linear recurrences), e.g. the number of speciic digital patterns, satisfy a central limit theorem. We provide asymptotic expansions for mean value and variance and prove a global and a local limit law.

In this article, we consider two models of directed polymers in random environment: a discrete model in a general random environment and a continuous model. We consider these models in dimension greater or equal to 3 and we suppose that the normalized partition function is bounded in L (the ”high” temperature case). Under these assumptions, Sinai proved in [11] a local limit theorem for the dis...

We consider Euclid’s gcd algorithm for two integers (p, q) with 1 ≤ p ≤ q ≤ N , with the uniform distribution on input pairs. We study the distribution of the total cost of execution of the algorithm for an additive cost function d on the set of possible digits, asymptotically for N → ∞. For any additive cost of moderate growth d, Baladi and Vallée obtained a central limit theorem, and –in the ...

We prove a local limit theorem for the area of the positive exursion of random walks with zero mean and finite variance. Our main result complements previous work of Caravenna and Chaumont, Sohier, as well as Kim and Pittel.