Fractional Moments of Small-Ball Masses for the Stochastic Heat Flow

Abstract

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.

25 pages