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- W2891384423 abstract "We consider a {it{Gaussian multiplicative chaos}} (GMC) measure on the classical Wiener space driven by a smoothened (Gaussian) space-time white noise. For $dgeq 3$ it was shown in cite{MSZ16} that for small noise intensity, the total mass of the GMC converges to a strictly positive random variable, while larger disorder strength (i.e., low temperature) forces the total mass to lose uniform integrability, eventually producing a vanishing limit. Inspired by strong localization phenomena for log-correlated Gaussian fields and Gaussian multiplicative chaos in the finite dimensional Euclidean spaces (cite{MRV16,BL18}), and related results for discrete directed polymers (cite{V07,BC16}), we study the endpoint distribution of a Brownian path under the {it{renormalized}} GMC measure in this setting. We show that in the low temperature regime, the energy landscape of the system freezes and enters the so called {it{glassy phase}} as the entire mass of the Cesaro average of the endpoint GMC distribution stays localized in few spatial islands, forcing the endpoint GMC to be {it{asymptotically purely atomic}} (cite{V07}). The method of our proof is based on the translation-invariant compactification introduced in cite{MV14} and a fixed point approach related to the cavity method from spin glasses recently used in cite{BC16} in the context of the directed polymer model in the lattice." @default.
- W2891384423 created "2018-09-27" @default.
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- W2891384423 date "2018-08-15" @default.
- W2891384423 modified "2023-09-27" @default.
- W2891384423 title "Localization of the Gaussian multiplicative chaos in the Wiener space and the stochastic heat equation in strong disorder" @default.
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