Quansheng Liu

activity

20082022

most citedExponential inequalities for martingales and asymptotic properties of the free energy of directed polymers in random environment

70 citations · 207 across the 35 of their papers we have counts for

collaborators

Showing 2022Show all

4 papers · 1 filter

math.PR2022★ 1 cited

Moderate deviations and local limit theorems for the coefficients of random walks on the general linear group

Hui Xiao, Ion Grama, Quansheng Liu

Consider the random walk $G_{n} := g_{n} \dots g_{1}$ , $n \geq 1$ , where $(g_{n})_{n \geq 1}$ is a sequence of independent and identically distributed random elements with law $μ$ on the…

math.PR2022★ 2 cited

Edgeworth expansion for the coefficients of random walks on the general linear group

Hui Xiao, Ion Grama, Quansheng Liu

Let $(g_{n})_{n \geq 1}$ be a sequence of independent and identically distributed random elements with law $μ$ on the general linear group $GL (V)$ , where $V = R^{d}$ . Con…

math.PR2022

Edgeworth expansion and large deviations for the coefficients of products of positive random matrices

Hui Xiao, Ion Grama, Quansheng Liu

Consider the matrix products $G_{n} := g_{n} \dots g_{1}$ , where $(g_{n})_{n \geq 1}$ is a sequence of independent and identically distributed positive random $d \times d$ matrices. Under…

math.PR2022★ 1 cited

Cramér's moderate deviations for martingales with applications

Xiequan Fan, Qi-Man Shao

Let $(ξ_{i}, F_{i})_{i \geq 1}$ be a sequence of martingale differences. Set $X_{n} = \sum_{i = 1}^{n} ξ_{i}$ and $⟨ X ⟩_{n} = \sum_{i = 1}^{n} E (ξ_{i}^{2} ∣ F_{i - 1}) .$ …