Math Courses

# Probability and Statistical Mechanics. Preliminary course.

## by Lu Xu (GSSI)

Europe/Rome
Ex-ISEF/Building-Room D (GSSI)

### Ex-ISEF/Building-Room D

#### GSSI

20
Description

The course will cover the following basic notions in probability:

• Probability space, random variable and its distribution;
• Convergence of random variables (in probability, in law, almost surely);
• Gaussian variable and Gaussian vector;
• (Strong) law of large numbers (i.i.d. case);
• Central limit theorem (i.i.d. case);
• Brownian motion, Donsker’s invariance principle;
• Poisson distribution, Poisson process, Poisson point process;
• Law of large numbers & central limit theorem for Poisson (point) process.