Tel Aviv University 
Dear all,
Following the passover break, the Horowitz seminar renews its
activity this Monday with a talk by Mikhail Sodin.
NOTE THE SPECIAL END TIME! The talk will be longer than usual.
Speaker: Mikhail Sodin, Tel Aviv University
Title: Random nodal portraits
Date: Monday, April 16
Time: from 14:30 to 16:00!
Place: Schreiber 309
We describe the progress in understanding the zero sets of smooth
Gaussian random functions of several real variables. The primary
examples are various ensembles of Gaussian real-valued polynomials
(algebraic or trigonometric) of large degree, and smooth Gaussian
functions on the Euclidean space with translation-invariant
distribution. The fundamental question is the one on the asymptotic
behaviour of the number of connected components of the zero set. This
can be viewed as a statistical version of Hilbert's 16th problem.
We start with an intriguing heuristics suggested by Bogomolny and
Schmit, which relates nodal portraits of 2D Gaussian monochromatic
waves to bond percolation on the square lattice. Then we explain how
Ergodic Theorem and rudimentary harmonic analysis help to find the
order of growth of the typical number of connected components of the
zero set. We will mention a number of basic questions, which remain
widely open.
The talk is based on joint works with Fedor Nazarov.
Best regards,


Seminar webpage:
Technion Math Net-2 (TECHMATH2)
Editor: Michael Cwikel   <> 
Announcement from: Ron Peled   <>