TY - JOUR

T1 - Eldan’s Stochastic Localization and Tubular Neighborhoods of Complex-Analytic Sets

AU - Klartag, Bo’az

N1 - Publisher Copyright:
© 2017, Mathematica Josephina, Inc.

PY - 2018/7/1

Y1 - 2018/7/1

N2 - 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.

AB - 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.

KW - Complex varieties

KW - Gaussian measure

KW - Stochastic processes

KW - Tubular neighborhoods

UR - http://www.scopus.com/inward/record.url?scp=85021805589&partnerID=8YFLogxK

U2 - 10.1007/s12220-017-9894-0

DO - 10.1007/s12220-017-9894-0

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AN - SCOPUS:85021805589

VL - 28

SP - 2008

EP - 2027

JO - Journal of Geometric Analysis

JF - Journal of Geometric Analysis

SN - 1050-6926

IS - 3

ER -