Course Identification

- Most exercises will be theoretical, but there will be some numerical exercises.
- Previous requirements: calculus and linear algebra, basic knowledge of probability theory. Knowledge of MATLAB will be helpful.

The course will familiarize the students with various applications of statistical physics, using examples from various disciplines. Topics will include:

1. Markov processes and Random walks. Einstein’s derivation of the diffusion equation. Central limit theorem. Markov processes and application to Google Page Rank algorithm.

2. Langevin and Fokker-Planck equations. Escape over-a-barrier, with applications to chemical reactions and physics. Discrete Langevin equation approach to cell size control. Modeling stock market dynamics and the Black-Scholes equation.

3. Noise. Power-spectra, Wiener Khinchin theorem, Telegraph and 1/f noise.

4. Generalized Central Limit Theorem and Extreme Values Statistics. Generalized central limit theorem and Levy-stable distributions, with application to anomalous diffusion and Levy flights. Gumbel, Weibull and Frechet universality classes for Extreme Value Statistics.

5. Random matrix theory. Semi-circle law and Wigner's surmise, Girko's law for non-hermitian matrices, applications in nuclear physics and ecology (stability of networks).

6. Percolation theory. Epidemic spreading, continuum percolation and its application to random resistor networks (variable-range-hopping) and flow through porous media.

7. Anderson localization (time-permitting). Transfer matrix approach in 1d systems. Implications for electronic transport and light propagation in disordered media.

8. Glasses (time-permitting). Spin-glasses, aging and slow relaxations.

The purposes of this course is to familiarize you with a broad range of examples where randomness plays a
key role, develop an intuition for it, and get to the level where you may read a recent research paper on
the subject and be able to understand the terminology, the context and the tools used. This is in a sense
the "organizing principle" behind the various parts of the course: in all of them we are driven by applications where probability and statistical physics plays a fundamental role, and leads to exciting and often intriguing phenomena.

The course will follow:

Amir, Ariel. Thinking Probabilistically: Stochastic Processes, Disordered Systems, and Their Applications. Cambridge University Press, 2020.