6 papers
Gradient Mean-Field Dynamics with Measure-Valued States: Well-Posedness, Chaos, and Long-Time Stability
Anderson Melchor Hernandez
We study a stochastic mean-field interacting particle system whose state space is $\Y = \Tt^d \times \cP(U)$, where the first component represents a spatial variable and the second…
On a Central Limit Theorem and Sanov's principle for quantum neural networks
Anderson Melchor Hernandez
In this work, we study the fluctuations of a Mixture of Experts (MoE) generated by a quantum neural network trained via gradient flow on supervised learning problems. Our main resu…
-convergence of discrete energies modeling self-aggregation of stochastic particles
Luca Lussardi, Anderson Melchor Hernandez, Marco Morandotti
In this work, we demonstrate that a functional modeling the self-aggregation of stochastically distributed lipid molecules can be obtained as the -limit of a family of discrete…
Weighted heat kernel estimates: rate of convergence in Kolmogorov distance
Anderson Melchor Hernandez
This paper is concerned about random walks on random environments in the lattice . This model is analyzed through ergodicity in the form of the logarithmic Sobolev in…
Weighted Meyers estimates in perforated domains
Anderson M. Hernandez
The present work aims to provide Meyers estimates throughout a finer inner regularity theory in perforated domains. We also provide a hypercontractivity property on correctors when…
Coarsen entropy inequalities and its applications in quantitative stochastic homogenization
Anderson M. Hernandez
In this work, we study the validity of Entropy inequalities under decorrelation assumptions at large-scales, and also we study the problem of Weighted Meyers estimate in perforated…