Universal Fluctuations in the Tail Probability for d=2 Random Walks in Space-Time Random Environments

2025/08/21 by Ark, Franscesca, Hass, Jacob B., Corwin, Eric I.
#FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech)

paper · doi:10.48550/arxiv.2508.15999

Abstract

Many diffusive systems involve correlated random walkers due to a shared environment. Such systems can be modeled as random walks in random environments (RWRE). These models differ from classical diffusion in the behavior of the extremes -- the walkers that move the fastest or farthest. In spatial dimension d=1 RWRE models have been well studied numerically and analytically and exhibit universal behavior in the Kardar-Parisi-Zhang universality class. Here, we study discrete lattice RWRE models in d=2. We find that the tail probability exhibits a different universal scaling form, which is nevertheless characterized by the same coefficient, λ_ext, as in the d=1 case. We observe a critical scaling regime for fluctuations in the tail probability at positions that scale linearly in time.

Citations

• Random walks in space-time random media in all spatial dimensions: the full subcritical fluctuation regime
• Super-Universal Behavior of Outliers Diffusing in a Space-Time Random Environment
• Universal KPZ Fluctuations for Moderate Deviations of Random Walks in Random Environments
• Hierarchy of KPZ limits arising from directed random walk models in random media
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