论文标题
单纯偏见的相邻步行的流体动力限制和截止
Hydrodynamic limit and cutoff for the biased adjacent walk on the simplex
论文作者
论文摘要
我们在$ n-1 $ $ n $ n-1 $订购的粒子的混合时间的$ n $中调查了渐近造成的时间。该动力学包括根据独立泊松的重新采样，根据其最近邻居形成的段的概率度量。在重新采样概率度量对称的情况下，获得了混合时间的渐近性，并存在截止现象。在目前的工作中，我们专注于该模型的不对称版本，并建立了截止现象。我们分析的一个重要部分在于流体动力学极限的推导，该限制由非线性汉密尔顿 - 雅各比方程（具有退化边界条件）给出。
We investigate the asymptotic in $N$ of the mixing times of a Markov dynamics on $N-1$ ordered particles in an interval. This dynamics consists in resampling at independent Poisson times each particle according to a probability measure on the segment formed by its nearest neighbours. In the setting where the resampling probability measures are symmetric, the asymptotic of the mixing times were obtained and a cutoff phenomenon holds. In the present work, we focus on an asymmetric version of the model and we establish a cutoff phenomenon. An important part of our analysis consists in the derivation of a hydrodynamic limit, which is given by a non-linear Hamilton-Jacobi equation with degenerate boundary conditions.
