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master degree course in MATHEMATICS

Course year 1
Teaching units Unit Sistemi di particelle interagenti
Models and Application (lesson)
  • TAF: Compulsory subjects, characteristic of the class SSD: MAT/07 CFU: 6
Teachers: Gioia CARINCI
Exam type oral
Evaluation final vote
Teaching language Italiano
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The course aims at introducing to the study of stochastic models for complex systems consisting of an high number of interacting agents (particles, spins or individuals in a population) with applications in several scientific fields.

Admission requirements

he content of a standard basic course of Probability theory of an undergraduate program in Mathematics.

Course contents

Markov chains. Classification of states (recurrence and transience), periodicity. Continuous-time Markov processes. Generator and Semigroup. Random Walks.

Construction of the generator of an interacting particle system. Stationary measure, symmetries and reversibility. Duality.

Systems of independent random walkers. Exclusion process. Inclusion process. Voter model. Contact process. Spin systems.

Introduction to hydrodynamic limits.

Teaching methods

Combination of asynchronous (recorded) lectures and synchronous (streaming) online classes. Slides and graphics tablets will be used. The supply of face-to-face classes will be evaluated on the base of the evolution of the COVID19 emergency situation.

Assessment methods

Oral exam at the end of the course, through which both theoretical knowledge and the ability to solve exercises will be assessed. This will be given in the online or in the face-to-face form depending on the evolution of the COVID19 emergency situation.

Learning outcomes

Learn the basic techniques of interacting particle systems and Markov process theory.
Being able to apply these techniques to the Voter model, exclusion process and related models.
Acquire the adequate technical language and the mathematical formalism. Being able to read a research literature in this area.


Sheldom Ross, Stochastic processes, John Wiley and Sons, Inc.

T.M. Liggett: Interacting Particle Systems. 1985, Springer