Eldan's stochastic localization and tubular neighborhoods of complex-analytic sets

2017/02/08 by Klartag, Bo'az · 2 citations
#Complex Variables (math.CV) #FOS: Mathematics #Metric Geometry (math.MG) #Probability (math.PR)

paper · doi:10.48550/arxiv.1702.02315

Abstract

Let Z be the zero set of a holomorphic map from Cⁿ to C^k. Assume that Z is non-empty. We prove that for any r > 0, the Gaussian measure of the Euclidean r-neighborhood of Z is at least as large as the Gaussian measure of the Euclidean r-neighborhood of E, where E is any (n-k)-dimensional, affine, complex subspace whose distance from the origin is the same as the distance of Z from the origin.

Cited by

• Perspectives on Stochastic Localization
• Functional Stochastic Localization

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