5 papers
The Asayama-Matsumoto conjecture and a refined discrepancy bound
Alessio Basti, Tommaso Cremaschi
Every -vertex plane triangulation admits a polychromatic red--blue vertex coloring with discrepancy at most $n-2\ceil{n/3}\le\floor{n/3}$, resolving a conjecture of Asayama and…
Markov Chain Approximation of Sticky Diffusions and Hamilton-Jacobi-Bellman Equations on Networks
Alessio Basti, Jules Berry, Fabio Camilli
We propose a discrete Markov-chain approximation of diffusion processes on networks with both Kirchhoff and sticky vertex conditions. Stickiness is modeled by a probabilistic resid…
Kolmogorov -entropy of numerical solutions for scalar conservation laws with convex flux
Fabio Ancona, Alessio Basti, Fabio Camilli
Building on the information-theoretic perspective of P.~D.~Lax [\textit{Proc.\ Sympos., Math.\ Res.\ Center, Univ.\ Wisconsin}, 1978], we establish a two-sided quantitative compact…
A Mean Field Games Perspective on Evolutionary Clustering
Alessio Basti, Fabio Camilli, Adriano Festa
We propose a control-theoretic framework for evolutionary clustering based on quasi-stationary Mean Field Games. Each cluster is represented by a probability density whose evolutio…
Estimates for Numerical Approximation of Convex Hamilton-Jacobi Equations
Alessio Basti, Fabio Camilli
We establish error estimates for monotone numerical schemes approximating convex Hamilton-Jacobi equations on the -dimensional torus. Using the adjoint method and semiconc…