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- W2579248413 abstract "We study the volume and Euler characteristic of codimension $r in {1,dots,n}$ random submanifolds in a dimension $n$ manifold $M$. First, we consider Riemannian random waves. That is $M$ is a closed Riemannian manifold and we study the common zero set $Z_lambda$ of $r$ independent random linear combinations of eigenfunctions of the Laplacian associated to eigenvalues smaller than $lambdageq 0$. We compute estimates for the mean volume and Euler characteristic of $Z_lambda$ as $lambda$ goes to infinity.We also consider a model of random real algebraic manifolds. In this setting, $M$ is the real locus of a projective manifold defined over the reals. Then, we consider the real vanishing locus $Z_d$ of a random real global holomorphic section of $E otimes L^d$, where $E$ is a rank $r$ Hermitian vector bundle, $L$ is an ample Hermitian line bundle and both these bundles are defined over the reals. We compute the asymptotics of the mean volume and Euler characteristic of $Z_d$ as $d$ goes to infinity. In this real algebraic setting, we also compute the asymptotic of the variance of the volume of $Z_d$, when $1 leq r < n$. In this case, we prove asympotic equidistribution results for $Z_d$ in $M$." @default.
- W2579248413 created "2017-01-26" @default.
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- W2579248413 date "2016-11-24" @default.
- W2579248413 modified "2023-09-25" @default.
- W2579248413 title "Contributions to the study of random submanifolds" @default.
- W2579248413 hasPublicationYear "2016" @default.
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