Minimum Memory for Generating Rare Events

Cina Aghamohammdi and James P. Crutchfield

Complexity Sciences Center
Physics Department
University of California at Davis
Davis, CA 95616

ABSTRACT: We classify the rare events of structured, memoryful stochastic processes and use this to analyze sequential and parallel generators for these events. Given a stochastic process, we introduce a method to construct a new process whose typical realizations are a given process' rare events. This leads to an expression for the minimum memory required to generate rare events. We then show that the recently discovered classical-quantum ambiguity of simplicity also occurs when comparing the structure of process fluctuations.

Cina Aghamohammdi and James P. Crutchfield, “The Markov Memory for Generating Rare Events”, Physical Review E 95:3 (2017) 032101.
Santa Fe Institute Working Paper 16-10-022. [cand-mat.stat-mech].