92 citations · 273 across the 36 of their papers we have counts for
17 papers · 1 filter
The Gauss-Bonnet-Chern theorem: a probabilistic perspective
Liviu I. Nicolaescu, Nikhil Savale
We prove that the Euler form of a metric connection on real oriented vector bundle over a compact oriented manifold can be identified, as a current, with the expectation of…
Random Morse functions and spectral geometry
Liviu I. Nicolaescu
We study random Morse functions on a Riemann manifold defined as a random Gaussian weighted superpositions of eigenfunctions of the Laplacian of the metric . The rando…
Complexity of random smooth functions on compact manifolds
Liviu I. Nicolaescu
We relate the distribution of eigenvalues of a random symmetric matrix in the Gaussian Orthogonal Ensemble to the distribution of critical values of a random linear combination of…
Pixelations of planar semialgebraic sets and shape recognition
Liviu I. Nicolaescu, Brandon Rowekamp
We describe an algorithm that associates to each positive real number and each finite collection of planar pixels of size a planar piecewise linear set with the…
The blowup along the diagonal of the spectral function of the Laplacian
Liviu I. Nicolaescu
We formulate a precise conjecture about the universal behavior near the diagonal of the spectral function of the Laplacian of a smooth compact Riemann manifold. We prove this conje…
Critical sets of random smooth functions on compact manifolds
Liviu I. Nicolaescu
Given a compact, -dimensional Riemann manifold and a large positive constant we denote by the subspace of spanned by the eigenfunctions of the La…