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Physics 510
Stochastic Processes in Physics
Birger Bergersen

Master Equation.
System size expansion.
Fokker-Planck equation.
Brownian particles.
Several variables, SIR-model.
Branching processes by Timothy Duty.
Absorbing boundaries.
Transformations, Blow torches.
Langevin approach.
Molecular motors by Rolf Luchsinger.
Lévy-stable distributions .
Quantum vs. classical magnets by Geordie Rose.
Pareto tail. Continuous time random walk.
Return time distribution. Continuous time random walk (continued).
Random walk in fractal time. Self-avoiding random walk .
1/f-noise by Alexandre Zagoskin.
Collective decision making in ant foraging. Suresh Pillai.
Flory theory.Edwards model..
Rescaled range analysis. Fractal Brownian motion.
Field theory methods I by Timothy Duty.
Field theory methods II by Timothy Duty.
Laser cooling by Jens Schmid.
Modelling intentionality: the gambler by Rik Blok.
The basics of derivative pricing in discrete time by Ernest Ho.
Stochastic Dynamics in Game Theory by Margarita Ifti.
Problem set 1
Problem set 2

Tutorial: 1. Boltzmann statistics


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Lecture 13.

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Lecture 10.

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Lectures 14,18.

M.E. Cates and S.J. Candau [1990], Statics and dynamics of wormlike surfactant micelles J.Phys.Cond Matter, 2 6869-92.
Lecture 13.

J.Feder, [1988] Fractals, Plenum.
Lecture 13.

W. Feller [1966] An introduction to probability theory and its application, Wiley. Vols I and II.
Lecture 15

T. Higuchi [1990], Relationship between the fractal dimension and the power law index for a time series: A numerical investigation, Physica D46 254-64 . Lecture 19.

F. Jülicher, A. Ajdari and J. Prost [1997], Modeling molecular motors, Rev. Mod. Physics 69 1269-81
Lecture 10.

M. Kimura [1955], Solution of a process of random genetic drift with a continuous model, Proc. National. Acandemy of Sciences 41 144-50.
Lecture 7.

R. Landauer [1988], Motion out of noisy states, J. Stat. Phys 53 233-48.
Lecture 8.

H F Lydall [1959], The distribution of employment incomes Econometrica 27, 110.
Lexture 13.

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Lecture 10.

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Lecture 13.

B. B. Mandelbrot and J. W. Van Ness [1968], fractional Brownian motion,fractional noises and applications, SIAM Review 10 422-37.
Lecture 19.

B. B. Mandelbrot [1997], Fractals and scaling in finance; discontinuity, concentration, risk, Springer.
Lecture 15.

M. Marsili and Y-C. Zhang [1997], Fluctuations around Nash equilibria in game theory, Physica A245 181-8 (1997).
Lecture 25.

M. Marsili and Y-C. Zhang, Stochastic dynamics in game theory, cond-mat/9801309
Lecture 25.

R.M. Mazo [1975], On the discrepancy between results of Nicolis and Saitô concerning fluctuations in chemical reactions, The Journal of Phys. Chem. 62 4244.
Problem 2.

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Lecture 13.

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Lecture 13.

E.W. Montroll and B.J. West [1987], On an enriched collection of stochastic processes, Capter 2 in E.W. Montroll and J.L. Lebowitz eds., Fluctuation Phenomena, North Holland.
Lectures 11, 14.

Y. Oono [1985], Adv. Chem. Phys. 61 301.
Lecture 18.

A. Ott, J.P. Bouchaud, D. Langevin and W. Urbach, Anomalous diffusion in "Living polymers"; A genuine Lévy flight, Phys.Rev. Lett. 65 2201-4 (1990).
Lecture 13.

V. Pareto [1968],The rise and fall of the elites, Bedminster Press, Introduction by H. L Zetterberg originally Un applicazione di teorie sociologiche', Revista Italiana di Sociologia 1901 402-456.
Lecture 13.

V. Pareto [1984], The transformation of democracy, translation of Trasformazione della democrazia Transaction books (Rutgers) with introduction by C. H. Powers.
Lecture 13.

H.-O. Peitgen and D. Saupe eds.[1985] , The science of fractal images, Springer. Articles by R.F. Voss and D. Saupe contains descriptions of how to produce fractal surfaces.
Lecture 19.

M. Plischke and B. Bergersen [1994], Equilibrium Statistical Physics, xi+356 pages, 2nd Ed World Scientific.
Lectures 15, 18.

J. Prost, J.-F. Chauwin, L. Peliti and Armad Ajdari [1994], Asymmetric pumping of particles, Phys. Rev. Lett. 72 2652.
Lecture 10.

H. Risken [1989], The Fokker-Planck equation; methods of solutions and applications, Springer.
Lectures 7-9.

H. Scher and E.W. Montroll E.W. [1975], Anomalous transit-time dispersion in amorphous solids Phys. Rev. B12 2455-77.
Lecture 14.

N.G. van Kampen [1976], The expansion of the master equation, Adv. Chem. Phys. 34 245 (1976).
Lectures 1-3, 5.

N.G. van Kampen, Stochastic processes in physics and chemistry, North Holland (1981).
Lectures 1-5,7,9

N.G. van Kampen [1993], Short first passage times, J. Stat. Phys. 70 15-23.
Lecture 8.

N.G. van Kampen [1987], Diffusion in inhomogeneous media, Z. Phys. B-Condensed matter 68 135-8.
Lecture 8.

N.G. van Kampen [1981], Ito versus Stratanovich, J. of Statistical Physics 24 175-187.
Lecture 9.

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Birger Bergersen