# Scaling limit for trap models on $\\mathbb{Z}^d$

Source: [Scaling limit for trap models on $\\mathbb{Z}^d$](<https://www.sota2.com/research/paper/68fa2ad21e209131ce84121a>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-24T13:49:02.747Z

Authors: G\\'erard Ben Arous, Ji\\v{r}\\'i \\v{C}ern\\'y

Published: 2006-06-28T12:59:46.000Z

## Abstract

We give the \`\`quenched'' scaling limit of Bouchaud's trap model in ${d\\ge 2}$. This scaling limit is the fractional-kinetics process, that is the time change of a $d$-dimensional Brownian motion by the inverse of an independent $\\alpha$-stable subordinator.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/math/0606719>)

[PDF](<https://arxiv.org/pdf/math/0606719.pdf>)