Antti Kupiainen

Basic properties of critical lognormal multiplicative chaos

We study one-dimensional exact scaling lognormal multiplicative chaos measures at criticality. Our main results are the determination of the exact asymptotics of the right tail of the distribution of the total mass of the measure, and an almost sure upper bound for the modulus of continuity of the cumulative distribution function of the measure. We also find an almost sure lower bound for the increments of the measure almost everywhere with respect to the measure itself, strong enough to show that the measure is supported on a set of Hausdorff dimension 0.

Renormalization of Generalized KPZ Equation

We use Renormalization Group to prove local well posedness for a generalized KPZ equation introduced by H. Spohn in the context of stochastic hydrodynamics. The equation requires the addition of counter terms diverging with a cutoff

Fluctuation relation for qubit calorimetry

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Renormalizability of Liouville quantum field theory at the Seiberg bound

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Liouville Quantum Gravity on the Riemann Sphere

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Renormalizability of Liouville Quantum Gravity at the Seiberg bound

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