Stochastic phenomena, the description of which involves randomness, are ubiquitous in physics, chemistry, biology and beyond (information theory, computer science, economy etc.). The goal is to equip students with the essential tools for their modeling and understanding. The course starts with a probability bootstrap with emphasis on large deviations, establishing a bridge with statistical physics approaches. Markov processes, Langevin and Fokker-Planck equations are then presented, together with the stochastic differential equation framework and stochastic calculus (Stratonovich versus Ito-Döblin rules). The linear-response theory features, found along the way, will be put in a broader perspective. The second half of the course is devoted to fluctuation theorems, first passage properties. Follows an introduction to functionals of Brownian motion and the Feynman-Kac formula.

1. Few useful concepts of probability theory 2. Introduction to Langevin equation 3. Markov processes and Master equation 4. Stochastic differential equations 5. Fokker-Planck equation 6. Functionals of stochastic processes

READING MATERIALS: • The Fokker-Planck Equation: Methods of Solutions and Applications, H. Risken, Springer. • Stochastic processes in physics and chemistry, N. G. van Kampen, Elsevier. • Handbook of stochastic methods, C. W. Gardiner, Springer. STUDY MATERIALS: can be found at https://physics-complex-systems.fr/cursus.html

Modalità di esame: Prova scritta (in aula);

Exam: Written test;

...

Gli studenti e le studentesse con disabilità o con Disturbi Specifici di Apprendimento (DSA), oltre alla segnalazione tramite procedura informatizzata, sono invitati a comunicare anche direttamente al/la docente titolare dell'insegnamento, con un preavviso non inferiore ad una settimana dall'avvio della sessione d'esame, gli strumenti compensativi concordati con l'Unità Special Needs, al fine di permettere al/la docente la declinazione più idonea in riferimento alla specifica tipologia di esame.