Course Identification

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.