论文标题
量子Lévy过程和量子随机换位的截止曲线
Cutoff profiles for quantum Lévy processes and quantum random transpositions
论文作者
论文摘要
我们考虑了在免费正交量子组上的布朗运动的天然类似物，并证明它在时间$ n \ ln（n）$时表现出截止。然后，我们研究实际线上的诱导经典过程，并计算其原子和密度。这使我们能够找到临界概况，其中涉及免费的泊松分布和半圆法。我们证明了量子排列和量子随机换位的相似结果。
We consider a natural analogue of Brownian motion on free orthogonal quantum groups and prove that it exhibits a cutoff at time $N\ln(N)$. Then, we study the induced classical process on the real line and compute its atoms and density. This enables us to find the cutoff profile, which involves free Poisson distributions and the semi-circle law. We prove similar results for quantum permutations and quantum random transpositions.
