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.