The Markov Memory for Generating Rare Events

TL;DR

This paper introduces a method to classify and generate rare events in structured stochastic processes, revealing the minimum memory needed and uncovering a classical-quantum ambiguity in process fluctuations.

Contribution

It provides a novel framework for analyzing rare events and their memory requirements, extending the understanding of process complexity and quantum-classical ambiguities.

Findings

A new process construction for generating rare events

An expression for minimum memory needed for rare event generation

Discovery of classical-quantum ambiguity in process fluctuations

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.