Gaussian limits for subcritical chaos
Copyright policy )Gaussian limits for subcritical chaos
We present a simple criterion, only based on second moment assumptions, for the convergence of polynomial or Wiener chaos to a Gaussian limit. We exploit this criterion to obtain new Gaussian asymptotics for the partition functions of two-dimensional directed polymers in the sub-critical regime, including a singular product between the partition function and the disorder. These results can also be applied to the KPZ and Stochastic Heat Equation. As a tool of independent interest, we derive an explicit chaos expansion which sharply approximates the logarithm of the partition function.
35 pages, 1 figure. Final version published in EJP
KPZ equation, Edwards-Wilkinson fluctuations, Probability (math.PR), Primary: 60F05, Secondary: 82B44, 35R60, central limit theorem, FOS: Physical sciences, Central limit and other weak theorems, Mathematical Physics (math-ph), central limit theorem; directed polymer in random environment; Edwards-Wilkinson fluctuations; KPZ equation; polynomial chaos; stochastic heat equation; Wiener chaos;, polynomial chaos, stochastic heat equation, Wiener chaos, directed polymer in random environment, FOS: Mathematics, PDEs with randomness, stochastic partial differential equations, Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics, Mathematics - Probability, Mathematical Physics
KPZ equation, Edwards-Wilkinson fluctuations, Probability (math.PR), Primary: 60F05, Secondary: 82B44, 35R60, central limit theorem, FOS: Physical sciences, Central limit and other weak theorems, Mathematical Physics (math-ph), central limit theorem; directed polymer in random environment; Edwards-Wilkinson fluctuations; KPZ equation; polynomial chaos; stochastic heat equation; Wiener chaos;, polynomial chaos, stochastic heat equation, Wiener chaos, directed polymer in random environment, FOS: Mathematics, PDEs with randomness, stochastic partial differential equations, Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics, Mathematics - Probability, Mathematical Physics
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