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- W2892041387 abstract "We continue with the study of the mollified stochastic heat equation in $dgeq 3$ given by $d u_{epsilon,t}=frac 12Delta u_{epsilon,t}+ beta epsilon^{(d-2)/2} ,u_{epsilon,t} ,d B_{epsilon,t}$ with spatially smoothened cylindrical Wiener process $B$, whose (renormalized) Feynman-Kac solution describes the partition function of the continuous directed polymer. In an earlier work (cite{MSZ16}), a phase transition was obtained, depending on the value of $beta>0$ in the limiting object of the smoothened solution $u_epsilon$ as the smoothing parameter $epsilonto 0$ This partition function naturally defines a quenched polymer path measure and we prove that as long as $beta>0$ stays small enough while $u_epsilon$ converges to a strictly positive non-degenerate random variable, the distribution of the diffusively rescaled Brownian path converges under the aforementioned polymer path measure to standard Gaussian distribution." @default.
- W2892041387 created "2018-09-27" @default.
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- W2892041387 date "2017-10-02" @default.
- W2892041387 modified "2023-09-27" @default.
- W2892041387 title "Quenched central limit theorem for the stochastic heat equation in weak disorder" @default.
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