标题： 随机沙堆模型：精确采样和完全图 显示英文标题

标题： Stochastic Sandpile model: exact sampling and complete graph

摘要： 我们研究有限图上的随机沙堆模型的动力学，有两个主要结果。 首先，我们描述了一种在所有连通有限图上精确采样来自该模型平稳分布的过程，扩展了Levine和Liang对激活随机游走的结果。 然后，我们在顶点数趋于无穷大的完全图上研究该模型，并证明平稳密度趋于$1/2$。 在此过程中，我们引入了对该模型动力学的新观点，涉及活跃粒子和睡眠粒子，这可能具有独立的兴趣。 显示英文摘要

摘要： We study the dynamics of the Stochastic Sandpile Model on finite graphs, with two main results. First, we describe a procedure to exactly sample from the stationary distribution of the model in all connected finite graphs, extending a result obtained by Levine and Liang for Activated Random Walks. Then, we study the model on the complete graph with a number of vertices tending to infinity and show that the stationary density tends to $1/2$. Along the way, we introduce a new point of view on the dynamics of the model, with active and sleeping particles, which may be of independent interest.