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- W4313894753 abstract "Let $$mu $$ be a probability measure on $$textrm{GL}_d(mathbb {R})$$ and denote by $$S_n:= g_n cdots g_1$$ the associated random matrix product, where $$g_j$$ ’s are i.i.d.’s with law $$mu $$ . We study statistical properties of random variables of the form $$begin{aligned} sigma (S_n,x) + u(S_n x), end{aligned}$$ where $$x in mathbb {P}^{d-1}$$ , $$sigma $$ is the norm cocycle and u belongs to a class of admissible functions on $$mathbb {P}^{d-1}$$ with values in $$mathbb {R}cup {pm infty }$$ . Assuming that $$mu $$ has a finite exponential moment and generates a proximal and strongly irreducible semigroup, we obtain optimal Berry–Esseen bounds and the Local Limit Theorem for such variables using a large class of observables on $$mathbb {R}$$ and Hölder continuous target functions on $$mathbb {P}^{d-1}$$ . As particular cases, we obtain new limit theorems for $$sigma (S_n,x)$$ and for the coefficients of $$S_n$$ ." @default.
- W4313894753 created "2023-01-10" @default.
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- W4313894753 date "2023-01-09" @default.
- W4313894753 modified "2023-10-04" @default.
- W4313894753 title "Berry–Esseen Bounds with Targets and Local Limit Theorems for Products of Random Matrices" @default.
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- W4313894753 doi "https://doi.org/10.1007/s12220-022-01127-3" @default.
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