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Fractional Moments of Small-Ball Masses for the Stochastic Heat Flow
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We prove the logarithmic fractional-moment exponent for the mass of a shrinking ball under the critical two-dimensional stochastic heat flow. The proof builds on the geometric block decomposition of Gu and Tsai and introduces a fractional-product change of measure that preserves block independence and allows the fractional moments to be analyzed.
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Cited by 2 Pith papers
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Logarithmic intermittency of the critical 2D SHF
For the critical 2D stochastic heat flow, the minimal number of ε-balls carrying almost all mass is ε^{-2}(log 1/ε)^{-1/2+o(1)}, with the complementary sparsity bound holding simultaneously.
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Fractional moments of the Stochastic Heat Flow and 2D Directed Polymers
For 0<p<1, the p-th moment of the critical 2D SHF mass on a small ball is bounded by the second moment raised to a negative power whenever the second moment diverges, uniformly in time, disorder, and radius.
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