Stochastic processes in natural sciences 2023/2024
Lectures & classes:
Tuesdays 10:15 - 12:00
Fridays 14:15 – 16:00
Mid-term (28 Nov 2023) [Mid-term problems] [P1 solution] [P2 solution]
Exam (2 Feb 2024), 15:00 – 17:00
Group projects
Possible topics:- Pawula’s theorem: explained and illustrated with examples
- Quantum non-equilibrium dynamics: master equation and Fermi’s golden rule
- Lotka-Volterra: from mean field solution of the master equation to the equations for the averages, numerical solutions, etc.
- Kinetic description of coagulation in suspensions – Smoluchowski’s theory, hierarchy of kinetic equations and dynamics
- Fokker-Planck description of collective motion of active matter – kinetic equations, stability
- First passage times – definition and methods of computation of FPTs for Brownian systems
- Dynamic Light Scattering (DLS) in colloidal suspensions – stochastic description of scattered light intensity and relationship with diffusive properties
- The Black-Scholes equation and the role of stochastic processes in economic models
- Turing’s model of pattern formation – principles and resulting patterns
- Holtsmark's distribution and the statistics of the gravitational field arising from a random distribution of stars
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Class materials: (updated systematically)
- Lecture notes I: Introduction and discrete probability distributions
- Lecture notes II: Continuous probability distributions
- Lecture notes III: Example – random walks
- Lecture notes IV: Description of stochastic processes
- Lecture notes V: Markov processes
- Lecture notes VI: Master equation
- Lecture notes VII: Fokker-Planck equation (in progress)
- Lecture notes: References
Further reading: