Stochastic Scale Invariance and the KPZ formula
Vargas, Vincent (2009), Stochastic Scale Invariance and the KPZ formula, Columbia University Probability and Mathematical Physics Seminar, 2009-03, New-York, États-Unis
TypeCommunication / Conférence
Conference titleColumbia University Probability and Mathematical Physics Seminar
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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)
Subjects / KeywordsKPZ Equation
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