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math.CV2001
Local dimension-free estimates for volumes of sublevel sets of analytic functions
F. Nazarov, M. Sodin, A. Volberg
This is a companion to our previous paper. Here, we derive local dimension-free estimates for volumes of sub- and super-level sets of analytic functions of several variables.
math.CA2001
The geometric Kannan-Lovasz-Simonovits lemma, dimension-free estimates for volumes of sublevel sets of polynomials, and distribution of zeroes of random analytic functions
F. Nazarov, M. Sodin, A. Volberg
The goal of this paper is to attract attention of the reader to a dimension-free geometric inequality that can be proved using the classical needle decomposition. This inequality a…