REVIEW 1 cited by
Hole event for random holomorphic sections on compact Riemann surfaces
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
abstract
Let $X$ be a compact Riemann surface and $\mathcal L$ be a positive line bundle on it. We study the conditional zero expectation of all the holomorphic sections of $\mathcal L^n$ which do not vanish on $D$ for some fixed open subset $D$ of $X$. We prove that as $n$ tends to infinity, the zeros of these sections are equidistributed outside $D$ with respect to a probability measure $\nu$. This gives rise to a surprising forbidden set.
Forward citations
Cited by 1 Pith paper
-
Hole Phenomenon of Gaussian Analytic Functions with Power-exponential Weights
For every β>0, conditioning a power-exponential Gaussian analytic function to have no zeros in D(0,r) makes the scaled zero measure converge to a limit supported on {|z|=1}∪{|z|≥e^{1/β}}, avoiding {1<|z|<e^{1/β}}.
Discussion (0). Sign in to comment.