Sharp asymptotic -f(beta) ≍ exp(-pi/sigma^2(beta)) for the 2D directed polymer quenched free energy as beta ↓ 0.
Sharp moment and upper tail asymptotics for the critical 2d stochastic heat flow.preprint arXiv:2507.22029
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For microscopically slowed-down Gaussian fields and branching Brownian motions, the recentered maximum is tight at the T^{1−α} scale, and the second-order correction exhibits a phase transition at α=1/3.
Establishes sharp local extinction rates and transition scales for 2D SHF together with free-energy asymptotics for directed polymers in strong disorder.
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Sharp behavior of the free energy for the two-dimensional directed polymer model
Sharp asymptotic -f(beta) ≍ exp(-pi/sigma^2(beta)) for the 2D directed polymer quenched free energy as beta ↓ 0.
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For microscopically slowed-down Gaussian fields and branching Brownian motions, the recentered maximum is tight at the T^{1−α} scale, and the second-order correction exhibits a phase transition at α=1/3.
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Strong Disorder for Stochastic Heat Flow and 2D Directed Polymers
Establishes sharp local extinction rates and transition scales for 2D SHF together with free-energy asymptotics for directed polymers in strong disorder.