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

G\'erard Ben Arous; Ji\v{r}\'i \v{C}ern\'y

arxiv: math/0606719 · v2 · pith:JRNJNNJAnew · submitted 2006-06-28 · 🧮 math.PR · math-ph· math.MP

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

G\'erard Ben Arous , Ji\v{r}\'i \v{C}ern\'y This is my paper

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keywords limitscalingtrapalphabouchaudbrownianchangedimensional

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

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