KPZ in a multidimensional random geometry of multiplicative cascades
Ismael Bailleul
TL;DR
This paper extends the one-dimensional KPZ formula to a multidimensional setting within a random geometry framework, broadening the applicability of KPZ theory.
Contribution
It introduces a multidimensional extension of the KPZ formula based on multiplicative cascades, expanding the theoretical understanding of random geometries.
Findings
Extended KPZ formula to multiple dimensions
Connected KPZ with multiplicative cascades
Provided new tools for multidimensional random geometry analysis
Abstract
We show in this note how the one-dimensional KZP formula obtained by Benjamini and Schramm can be extended to a multidimensional setting.
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Taxonomy
TopicsStochastic processes and statistical mechanics · Geometry and complex manifolds · Random Matrices and Applications