6 papers
The Probabilistic Structure of Large Language Models
Adnan Aboulalaâ
This paper presents a probabilistic perspective on large language models (LLMs), developed with the aim of bringing together, in a single self-contained account, tools that are usu…
Random fields, large deviations and triviality in quantum field theory. Part II
Adnan Aboulalaa
The approach developed in the first part of this work, partly based on large deviations, led to the non-existence of interacting scalar fields as strong limits of regularized field…
Propagation of microlocal singularities for stochastic partial differential equations
Adnan Aboulalaa
Microlocal analysis techniques are extended and applied to stochastic partial differential equations (SPDEs). In particular, the Hörmander propagation of singularities theorem is s…
Random fields, large deviations and triviality in quantum field theory. Part I
Adnan Aboulalaa
The issue of the existence and possible triviality of the Euclidean quantum scalar field in dimension 4 is investigated by using some large deviations techniques. As usual, the fie…
On the quasi-invariance of the Wiener measure on path spaces and the anticipative integrals over a Riemannian manifold
Adnan Aboulalaa
Some parts of stochastic analysis on curved spaces are revisted. A concise proof of the quasi-invariance of the Wiener measure on the path spaces over a Riemannian manifold is pres…
Stochastic Hyperbolic Systems, Small Perturbations and Pathwise Approximation
Adnan Aboulalaa
This paper is devoted to the study of hyperbolic systems of linear partial differential equations perturbed by a Brownian motion. The existence and uniqueness of solutions are prov…