Probability

Probability is the branch of applied mathematics dealing with the  study of random phenomena.  As such, it is a key toolbox for today physicists in diverse fields, both theoretical (statistical physics, quantum physics.. ) and experimental. Indeed, a major trigger for the development of probability has been the need of correctly estimating errors in measurements.

The aim of the course is to set the basis of the theory and to introduce the some of most important tools to with some rigour but skipping most of technical details.

We will start by providing the basic concepts: probability spaces, random variables, distributions, independence, expected values, conditional expectation. Then we will discuss more refined results  and tools: entropy, random sums of random variables, the law of large numbers, central limit theorem and large deviations. A particular emphasis will be given to the study of models issued from physics, including random walks and branching processes.