Florian Angeletti

Presentation

I am currently working on the OCaml compiler at Inria Paris within the Cambium team as a research engineer. In particular, I am working on OCaml type system and its error message.

OCaml and software engineering

Type systems, error messages and user experience

In a strongly typed language like OCaml, the type system and the user are interlocked in a permanent dialectic discussion. It is therefore imporant to make this discussion as serene as possible. In particular, the formal type system needs to be able to explain its issues in a humanly understandable format.

Statistical physics research

Previously, I have worked as statistical physicist for few yeears, focusing on classical statistical physics with a touch of signal processing. I have worked with Hugo Touchette on the applications of large deviation theory to non-equilibrium physics systems.Another of my subjects of predilection was the study random variables with a matrix representation started during my thesis. During this thesis, I have worked at the interface between statistical physics and statistical signal processing under the supervision of Eric Bertin and Patrice Abry. Within the page of this site, you shall find a short presentation of my old research subjects, a full listing of my publications and also some scientific software libraries.

Research themes

Phase transition in signal analysis

Phase transition is a fundamental notion in statistical physics. Applied to signal processing, it leads to original interpretations of well-known signal processing phenomena. For instance, the linearization effect which appears in moments estimation can be linked to the glassy phase transition of the physics of disordered systems. This analogy with the physics of disordered systems can help us to define a critical moment for finitely sized system beyond which the empirical moment estimator is not faithful anymore. Similar idea can be applied in multifractal analysis.

Extreme statistics

Extreme statistics for i.i.d (independent identically distributed) random variables are well known. However, with the introduction of correlations or dependencies with the sisterly size breaks, these classical results break down. For instance, non-standard limit distributions may appear if one consider the maximum of i.i.d random variable raised to a power dependent on the system size

Matrix representation

If the behavior of i.i.d random variables is well understood, most of physically interesting systems does not belong to this restrictive category. Unfortunately, non-i.i.d random variables are hard to describe generically. It is therefore useful to construct intermediary models between the walled garden of i.i.d. random variables and the wild world of fully dependent random variables. In this context, matrix-correlated random variables provide an interesting compromise. These random variables preserve the structure product of the joint probability density and introduce correlation due to the non-commutativity of the matrix product. Moreover, these random variables with a matrix representation can also be described as non-homogeneous Hidden Markov Model. These dual representations open interesting perspectives in both signal processing and statistical physics.

Large deviations theory

Large deviation theory studies the behavior of families of random variables far away from their concentration point. This point of view is complementary to the classical fluctuation theorem while the central limit theorem or the law of large numbers. One possible application for this theory is the question of the behavior of the sums of strongly correlated random variables far away from their concentrations points.