Trap models with vanishing drift: Scaling limits and aging regimes

TL;DR

This paper investigates trap models on integers with diminishing drift, revealing three regimes of long-term behavior, including a novel limit process, through scaling limits and aging analysis.

Contribution

It introduces a comprehensive analysis of trap models with vanishing drift, identifying new regimes and a previously unobserved limit process.

Findings

Three distinct aging regimes identified

A new limit process discovered in one regime

Scaling limits depend on trap tail behavior and drift strength

Abstract

We discuss the long term behaviour of trap models on the integers with asymptotically vanishing drift, providing scaling limit theorems and ageing results. Depending on the tail behaviour of the traps and the strength of the drift, we identify three different regimes, one of which features a previously unobserved limit process.