Title:
Transportation to random zeroes
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Abstract:
We consider the zeroes of the random Gaussian entire function.
A canonical random partition of the complex plane to random cells
of equal area will be is assigned to this random ensemble.
We find three characteristic exponents 1, 8/5 and 4 related to
this partition. For example, the exponent 8/5 gives the rate
of exponential decay e^{-8/5 R} of the event that a given point
lies at a distance larger than R from the random zero to which
it will be attracted by the gradient flow.
The exponents 1 and 4 will also be explained.