Random complex zeroes, III. Decay of the hole probability
Sodin, Mikhail ; Tsirelson, Boris
arXiv, 0312258 / Harvested from arXiv
Text on arXiv
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).
Publié le : 2003-12-12
Classification:  Mathematics - Complex Variables,  Mathematical Physics,  Mathematics - Probability,  30B20,  30C15, 60G60, 82B10 
@article{0312258,
     author = {Sodin, Mikhail and Tsirelson, Boris},
     title = {Random complex zeroes, III. Decay of the hole probability},
     journal = {arXiv},
     volume = {2003},
     number = {0},
     year = {2003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0312258}
}

Sodin, Mikhail; Tsirelson, Boris. Random complex zeroes, III. Decay of the hole probability. arXiv, Tome 2003 (2003) no. 0, . http://gdmltest.u-ga.fr/item/0312258/