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 -