## Research interests

I am attracted by comprehending how **fluctuations** arise in **out-of-equilibrium systems.** In particular, I am interested in developing **methods** to understand both the **likelihood** of these fluctuations and the **physical mechanisms** that generate them.

Many of the tools and mathematical techniques I use are inherited from the theory of large deviations: a branch of probability theory that deals with sums of random variables which decay exponential fast in the the system size, e.g., time for nonequilibrium systems.

I list here topics and project I like and work on.

###### Probability of, and physical mechanisms behind, rare events

Fluctuations arise in (finite size) random processes. Here, by means of large deviation theory, one can estimate their likelihood to appear.

Another interesting question is to understand the physical processes that generate these fluctuations. Once this is made clear, one could also develop tools to *control* the appearance of fluctuations.

###### Stochastic reset processes and stochastic efficiency

These are processes that have the property of being re-initialised at random times to a specific initial condition. The queue at the front-office, or the motion of a protein in a cell are only two examples of the wide range of applications that reset processes have in modeling real-world scenarios.

The focus is again on studying their fluctuations by means of large deviation theory. Recently, we worked on ratio observables, showing that their large deviations have universal features: differentiability, and tails bounded from above. In particular, we noticed the lack of a maximum, which is instead characteristic in the large deviations of the stochastic efficiency (also a ratio observable). This opened new research horizons...

###### Current large deviations in nonreversible processes: speed and accuracy of sampling

A nonreversible Markov process having the same invariant measure of a reversible one is known to converge faster to the stationary distribution. We gave a physical interpretation of this form of acceleration in terms of currents associated with the fluctuations of empirical estimators using the level 2.5 of large deviations, which characterizes the likelihood of density and current fluctuations in Markov processes.

As acceleration is not all when it comes to the numerical sampling of stationary distributions, our next step is to try to probe the accuracy of these nonreversible processes by means of large deviation methods.

###### Random walks on random graphs

Random walks on random graphs are not only a good model of disease spreading and information retrieval, but also a good playground to study, analytically and numerically, the *interplay between two sources of randomness*: the dynamical process itself, and the environment that hosts it.

For instance, a dynamical phase transition in additive observables, e.g. the mean degree visited, or the entropy production of the random walk, appears. As mean field tools are not of great help, we make use of other techniques, such as *conditioning on rare events*, *stochastic adaptive algorithms*, and *replica calculations*, to gain new insights.

###### Self-interacting diffusions

Self-interacting diffusions are processes with long-range interactions in time (*memory*). This is encoded in the drift of the process, as a dependence on the empirical occupation measure. These are as tough as rich processes to deal with. The goal is to develop a theory of their fluctuations.