Math Courses

Probability and Statistical Mechanics. Preliminary course.

by Lu Xu (GSSI)

Ex-ISEF/Building-Room D (GSSI)

Ex-ISEF/Building-Room D



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.