Eldan’s Stochastic Localization and Tubular Neighborhoods of Complex-Analytic Sets

Bo’az Klartag*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

Let f: Cn→ Ck be a holomorphic function and set Z= f- 1(0). Assume that Z is non-empty. We prove that for any r> 0 , γn(Z+r)≥γn(E+r),where Z+ r is the Euclidean r-neighborhood of Z; γn is the standard Gaussian measure in Cn, and E⊆ Cn is an (n- k) -dimensional, affine, complex subspace whose distance from the origin is the same as the distance of Z from the origin.

Original languageEnglish
Pages (from-to)2008-2027
Number of pages20
JournalJournal of Geometric Analysis
Volume28
Issue number3
DOIs
StatePublished - 1 Jul 2018

Funding

FundersFunder number
European Research Council
European Commission305629

    Keywords

    • Complex varieties
    • Gaussian measure
    • Stochastic processes
    • Tubular neighborhoods

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