Abstract. We study the asymptotic distribution of critical values of random holomorphic sections sn ∈ H0(Mm, Ln) of powers of a positive line bundle (L, h) → (M,ω) on a general Kähler manifold of dimension m. By critical value is meant the value of |s(z)|hn at a critical point where ∇hsn(z) = 0, where ∇h is the Chern connection. The distribution of critical values of sn is its empirical measure. Two main ensembles are considered: (i) the normalized Gaussian ensembles so that E ||sn||2L2 = 1 and (ii) the spherical ensemble defined by Haar measure on the unit sphere SH0(M,Ln) ⊂ H0(M,Ln) with ||sn||2L2 = 1. The main result is that the expected distributions of critical values in both the normalized Gaussian ensemble and the spherical ensem...
We define a Gaussian measure on the space H ) of almost holomorphic sections of powers of an ample l...
We obtain formulae for the expected number and height distribution of critical points of smooth isot...
We study the limiting distribution of critical points and extrema of random spherical harmonics, in ...
We examine the expected number N critN,h of critical points of random holomorphic sections of positi...
We study two conditional expectations: K-n (z vertical bar p) of the expected density of critical po...
ABSTRACT. Given a compact, connected Riemann manifold without boundary (M, g) of dimensionm and a la...
We study the limiting distribution of critical points and extrema of random spherical harmonics, in ...
Let $n\geq 2$ and $r\in \{1, \cdots, n-1\}$ be integers, $M$ be a compact smooth K\"ahler manifold o...
In this thesis we prove that as N goes to infinity, the scaling limit of the correlation between cri...
We study here the random fluctuations in the number of critical points with values in an interval I ...
We study here the random fluctuations in the number of critical points with values in an interval I ...
We study here the random fluctuations in the number of critical points with values in an interval I ...
We study here the random fluctuations in the number of critical points with values in an interval I ...
Final version, published in Trans. Amer. Math. Soc.International audienceLet $\mathcal{X}$ be a comp...
Final version, published in Trans. Amer. Math. Soc.International audienceLet $\mathcal{X}$ be a comp...
We define a Gaussian measure on the space H ) of almost holomorphic sections of powers of an ample l...
We obtain formulae for the expected number and height distribution of critical points of smooth isot...
We study the limiting distribution of critical points and extrema of random spherical harmonics, in ...
We examine the expected number N critN,h of critical points of random holomorphic sections of positi...
We study two conditional expectations: K-n (z vertical bar p) of the expected density of critical po...
ABSTRACT. Given a compact, connected Riemann manifold without boundary (M, g) of dimensionm and a la...
We study the limiting distribution of critical points and extrema of random spherical harmonics, in ...
Let $n\geq 2$ and $r\in \{1, \cdots, n-1\}$ be integers, $M$ be a compact smooth K\"ahler manifold o...
In this thesis we prove that as N goes to infinity, the scaling limit of the correlation between cri...
We study here the random fluctuations in the number of critical points with values in an interval I ...
We study here the random fluctuations in the number of critical points with values in an interval I ...
We study here the random fluctuations in the number of critical points with values in an interval I ...
We study here the random fluctuations in the number of critical points with values in an interval I ...
Final version, published in Trans. Amer. Math. Soc.International audienceLet $\mathcal{X}$ be a comp...
Final version, published in Trans. Amer. Math. Soc.International audienceLet $\mathcal{X}$ be a comp...
We define a Gaussian measure on the space H ) of almost holomorphic sections of powers of an ample l...
We obtain formulae for the expected number and height distribution of critical points of smooth isot...
We study the limiting distribution of critical points and extrema of random spherical harmonics, in ...