Diffusions interacting through a random matrix: universality via stochastic Taylor expansion
成果类型：
Article
署名作者：
Dembo, Amir; Gheissari, Reza
署名单位：
Stanford University; Stanford University; University of California System; University of California Berkeley; University of California System; University of California Berkeley
刊物名称：
PROBABILITY THEORY AND RELATED FIELDS
ISSN/ISSBN：
0178-8051
DOI：
10.1007/s00440-021-01027-7
发表日期：
2021
页码：
1057-1097
关键词：
摘要：
Consider (X-i (t)) solving a system of N stochastic differential equations interacting through a random matrix J = (J(ij)) with independent (not necessarily identically distributed) random coefficients. We show that the trajectories of averaged observables of (X-i (t)), initialized from some mu independent of J, are universal, i.e., only depend on the choice of the distribution J through its first and second moments (assuming e.g., sub-exponential tails). We take a general combinatorial approach to proving universality for dynamical systems with random coefficients, combining a stochastic Taylor expansion with a moment matching-type argument. Concrete settings for which our results imply universality include aging in the spherical SK spin glass, and Langevin dynamics and gradient flows for symmetric and asymmetric Hopfield networks.
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