Related papers: A survey on zeros of random holomorphic sections
We introduce a new method to study mixed characteristic deformation of line bundles. In particular, for sufficiently large smooth projective families $f : \mathscr{X} \to \mathscr{S}$ defined over the ring of $N$-integers…
In this paper, we study the unitarizations in the spaces of holomorphic sections of equivariant holomorphic line bundles over a bounded homogeneous domain under the action of a connected algebraic group acting transitively on the domain. We…
We show that almost all the zeros of any finite linear combination of independent characteristic polynomials of random unitary matrices lie on the unit circle. This result is the random matrix analogue of an earlier result by Bombieri and…
We study large partial sums, localized with respect to the sums of variances, of a sequence of centered random variables. An application is given to the distribution of prime factors of typical integers.
An approach is proposed for bounding the number of zeros that solutions of linear differential systems with polynomial coefficients may have. A bound is obtained in a special case which improves upon currently existing.
Sequences of discrete random variables are studied whose probability generating functions are zero-free in a sector of the complex plane around the positive real axis. Sharp bounds on the cumulants of all orders are stated, leading to…
This paper extends earlier work on the distribution in the complex plane of the roots of random polynomials. In this paper, the random polynomials are generalized to random finite sums of given "basis" functions. The basis functions are…
We show from a categorical point of view that probability measures on certain measurable or topological spaces arise canonically as the extension of probability distributions on countable sets. We do this by constructing probability monads…
Condition numbers of random polynomial systems have been widely studied in the literature under certain coefficient ensembles of invariant type. In this note we introduce a method that allows us to study these numbers for a broad family of…
This work is dedicated to studying holomorphic distributions on Grassmann manifolds and smooth quadric hypersurfaces. In special, we prove, under certain conditions, when the tangent and conormal sheaves of a distribution splits as a sum of…
Vector bundle cohomology represents a key ingredient for string phenomenology, being associated with the massless spectrum arising in string compactifications on smooth compact manifolds. Although standard algorithmic techniques exist for…
Motivated by the study of heterotic string compactifications on elliptically fibered Calabi-Yau manifolds, we present a procedure for testing semistability and identifying the decomposition type of degree zero holomorphic vector bundles…
We define integral geometric analogues of the Chern classes for real vector bundle on a smooth real variety. More precisely, we define the Chern densities of a real bundle. These densities are analogues of the Chern forms of a complex…
This is partly a survey article for Constructive Approximation's Special Issue on Approximation and Statistical Physics. It reviews results of B. Shiffman-S.Zelditch, R. Berman. S. Boucksom, D. Witt-Nystrom, T. Bloom, O. Zeitouni and others…
It is well known that the joint probability density of the eigenvalues of Gaussian ensembles of random matrices may be interpreted as a Coulomb gas. We review these classical results for hermitian and complex random matrices, with special…
We give asymptotic large deviations estimates for the volume inside a domain U of the zero set of a random polynomial of degree N, or more generally, of a holomorphic section of the N-th power of a positive line bundle on a compact Kaehler…
We give a survey concerning both very classical and recent results on the electrostatic interpretation of the zeros of some well-known families of polynomials, and the interplay between these models and the asymptotic distribution of their…
A systematic study of the probability distribution of superimposed random codes is presented through the use of generating functions. Special attention is paid to the cases of either uniformly distributed but not necessarily independent or…
Given a sequence of positive Hermitian holomorphic line bundles $(L_p,h_p)$ on a K\"ahler manifold $X$, we establish the asymptotic expansion of the Bergman kernel of the space of global holomorphic sections of $L_p$, under a natural…
We investigate the behavior of fractional derivatives of polynomials. In particular, we consider the locations and the asymptotic behaviour of their zeros and give bounds for their Mahler measure.