The Emergence of Laplace Universality in Correlated Processes

2024/10/30 by R. K. Singh, Singh, R. K., Stanislav Burov +1 · 1 citation
Economics, Econometrics and Finance · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Complex Systems and Time Series Analysis #FOS: Physical sciences #Soft Condensed Matter (cond-mat.soft) #Statistical Mechanics (cond-mat.stat-mech)

paper · pdf · doi:10.48550/arxiv.2410.23112

openalex publication_date 2024/10/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In transport processes across materials like glasses, living cells, and porous media, the probability density function of displacements exhibits exponential decay rather than Gaussian behavior. We show that this universal behavior of rare events, termed Laplace tails, emerges even when correlations and memory affect the dynamics. Using a renormalization-based approach, we demonstrate that correlations and memory do not suppress these tails but rather enhance their visibility, even at short timescales. The developed analytical framework refines the concept of correlations for rare events and enables the computation of effective parameters that govern Laplace tails in correlated processes. These findings suggest that correlations can serve as a tunable parameter to control the behavior of rare events in transport.

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