## B. Tsirelson | ## Random comples zeroes, III. Decay of the hole probability | ## Recent works |

Mikhail Sodin, Boris Tsirelson,

"Random comples zeroes, III. Decay of the hole probability."

math.CV/0312258.

Israel Journal of Mathematics **147**, 371-379 (2005).

Available online (free of charge) from e-print archive (USA):

arXiv.org/abs/math.CV/0312258/

or its Israeli mirror:

il.arXiv.org/abs/math.CV/0312258/

A research paper, 9 pages, bibl. 6 refs.

By a hole we mean a disc that contains no flat chaotic analytic zero
points (i.e. zeroes of a random entire function whose Taylor
coefficients are independent complex-valued Gaussian variables, and
the variance of the *k*-th coefficient is 1/*k*!). A given
disc of radius *r* has a probability of being a hole, - the hole
probability. We show that for large *r* the hole probability
decays as exp(-*cr*^{4}).

- Introduction.
- Proof of the lower bound in Theorem 1.
- Large deviations.
- Mean lower bound.
- Proof of Theorem 2.

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