Topology of random real hypersurfaces
Topology of random real hypersurfaces
These are notes of the mini-course I gave during the CIMPA summer school at Villa de Leyva, Colombia, in July $2014$. The subject was my joint work with Damien Gayet on the topology of random real hypersurfaces, restricting myself to the case of projective spaces and focusing on our lower estimates. Namely, we estimate from (above and) below the mathematical expectation of all Betti numbers of degree $d$ random real projective hypersurfaces. For any closed connected hypersurface $��$ of $\mathbb{R}^n$, we actually estimate from below the mathematical expectation of the number of connected components of these degree $d$ random real projective hypersurfaces which are diffeomorphic to $��$.
18 pages, notes of the course I gave during the CIMPA summer school at Villa de Leyva, Colombia, in July 2014
Probability (math.PR), 14P25, 60D05, matrices aleatorias, Real algebraic manifolds, Topology of real algebraic varieties, random matrices, 510, Polinomos aleatorios, Mathematics - Algebraic Geometry, Random polynomials, variedades algebraicas reales, real algebraic manifolds, FOS: Mathematics, [MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG], Geometric probability and stochastic geometry, [MATH]Mathematics [math], Random matrices, random polynomials, Algebraic Geometry (math.AG), Mathematics - Probability
Probability (math.PR), 14P25, 60D05, matrices aleatorias, Real algebraic manifolds, Topology of real algebraic varieties, random matrices, 510, Polinomos aleatorios, Mathematics - Algebraic Geometry, Random polynomials, variedades algebraicas reales, real algebraic manifolds, FOS: Mathematics, [MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG], Geometric probability and stochastic geometry, [MATH]Mathematics [math], Random matrices, random polynomials, Algebraic Geometry (math.AG), Mathematics - Probability
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