Estimates for simple random walks on fundamental groups of surfaces

关于随机游走渐近熵的谱

On the spectrum of asymptotic entropies of random walks

本研究聚焦自由群上随机游走在其商群诱导的随机游走，证明了诱导随机游走的渐近熵谱除最大值外无孤立点，丰富了群上随机游走的熵理论。

On the trace of branching random walks

We study branching random walks on Cayley graphs. A first result is that the trace of a transient branching random walk on a Cayley graph is a.s. transient for the simple random walk. In addition, it has a.s. critical percolation probability less than one and exponential volume growth. The proofs rely on the fact that the trace induces an invariant percolation on the family tree of the branching random walk. Furthermore, we prove that the trace is a.s. strongly recurrent for any (non-trivial) branching random walk. This follows from the observation that the trace, after appropriate biasing of …

有限群上的非时齐随机游走与随机整数分块矩阵的余核

Time-inhomogeneous random walks on finite groups and cokernels of random integer block matrices

研究有限群上非时齐随机游走的收敛性，通过谱方法给出收敛速率，并应用于随机整数矩阵余核的普适性定理。