Mikhail SODIN

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Local version of Theorem II:
The limiting constant ν(ρx) can be recovered by a double-scaling limit:
for a.e. x ∈ X and for each ɛ > 0,
lim
R→∞ lim
L→∞ P
1
volB(R) Nx, R
L ; fL − ν(ρx) > ɛ = 0
where N x, R
L ; fL is a number of connected components of the zero set
Z(fL) containing in the open ball centered at x of radius R/L,
volB(R) is the Euclidean volume of the ball of radius R in Rm .
Theorem II is “an integrated version” of the local result.
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