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Stochastic Scale Invariance and the KPZ formula

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Date
2009
Dewey
Probabilités et mathématiques appliquées
Sujet
KPZ Equation
Conference name
Columbia University Probability and Mathematical Physics Seminar
Conference date
03-2009
Conference city
New-York
Conference country
États-Unis
URI
https://basepub.dauphine.fr/handle/123456789/3672
Collections
  • CEREMADE : Publications
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Author
Vargas, Vincent
Type
Communication / Conférence
Abstract (EN)
In this talk, we will prove the KPZ equation (initially introduced in the framework of quantum gravity in 2 dimensions) for the limit lognormal measures introduced by Mandelbrot. More specifically, for a given set K, we will relate it's Hausdorff dimension under the Euclidian metric to it's Hausdorff dimension under the random metric induced by the limit lognormal measure. We will see how the notion of stochastic scale invariance is crucial in the derivation of the aforementioned relation. (Joint work with R. Rhodes)

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