资源分配的群体动力学中的相变
Phase transitions in crowd dynamics of resource allocation
摘要：
我们定义和研究一类资源分配过程中，$gN$代理，通过反复访问$N$资源，试图收敛到最佳配置，每个资源被占用最多一个代理。随着试剂的密度$g$的增加，该过程表现出从吸收相到活性相的相变。在后者中，即使资源的数量原则上对于所有代理（$g<1$）是足够的，系统也不会稳定到冻结配置。我们重铸这些过程中的零程相互作用粒子，研究分析的平均场动力学和调查在有限维数值的相变。我们发现一个很好的协议与随机固定能量沙堆的临界指数。在活动阶段缺乏协调也导致了一个不平凡的更快就是更慢的效果。
英文摘要：
We define and study a class of resources allocation processes where $gN$ agents, by repeatedly visiting $N$ resources, try to converge to optimal configuration where each resource is occupied by at most one agent. The process exhibits a phase transition, as the density $g$ of agents grows, from an absorbing to an active phase. In the latter, even if the number of resources is in principle enough for all agents ($g<1$), the system never settles to a frozen configuration. We recast these processes in terms of zero-range interacting particles, studying analytically the mean field dynamics and investigating numerically the phase transition in finite dimensions. We find a good agreement with the critical exponents of the stochastic fixed-energy sandpile. The lack of coordination in the active phase also leads to a non-trivial faster-is-slower effect.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
