arXiv subjects

S. Gaubert

Publications and source records attributed to S. Gaubert.

3 recordsLinked to original sources

arXiv2020

Probabilistic and mean-field model of COVID-19 epidemics with user mobility and contact tracing

We propose a detailed discrete-time model of COVID-19 epidemics coming in two flavours, mean-field and probabilistic. The main contribution lies in several extensions of the basic model that capture i) user mobility - distinguishing routing, i.e. change of residence, from commuting, i.e. daily mobility - and ii) contact tracing procedures. We confront this model to public data on daily hospitalizations, and discuss its application as well as underlying estimation procedures.

stat.AP↗

arXiv2012

Submodular spectral functions of principal submatrices of a hermitian matrix, extensions and applications

We extend the multiplicative submodularity of the principal determinants of a nonnegative definite hermitian matrix to other spectral functions. We show that if $f$ is the primitive of a function that is operator monotone on an interval containing the spectrum of a hermitian matrix $A$, then the function $I\mapsto {\rm tr} f(A[I])$ is supermodular, meaning that ${\rm tr} f(A[I])+{\rm tr} f(A[J])\leq {\rm tr} f(A[I\cup J])+{\rm tr} f(A[I\cap J])$, where $A[I]$ denotes the $I\times I$ principal submatrix of $A$. We discuss extensions to self-adjoint operators on infinite dimensional Hilbert space and to $M$-matrices. We discuss an application to CUR approximation of nonnegative hermitian matrices.

math.SP↗

arXiv2009

Perron-Frobenius theorem for nonnegative multilinear forms and extensions

We prove an analog of Perron-Frobenius theorem for multilinear forms with nonnegative coefficients, and more generally, for polynomial maps with nonnegative coefficients. We determine the geometric convergence rate of the power algorithm to the unique normalized eigenvector.

math.SP↗