Topic outline
About course - General
Topic outline
Generating function
Gaussian distribution and CLT
Intermediate asymptotics
Levy’s generalized CLT, the law of large numbers, examples for the emergence of power-law distributions
Random walks and the corresponding intermediate asymptotes
Random walks on a lattice in 1, 2 and 3 dimensions; Polya's problem
Discrete random walks on 3 dimensions and Polya’s problem; RW with non identical steps.
Random walks with non-identical steps and correlated random walks
Example of a correlated RW; Renewal processes
Forward recurrence time; Statistical aging
Occupation time; The continuous time random walk
CTRW propagator; The Fokker-Planck equation I
The Fokker-Planck equation II and the Langevin equation
Home assignment 1
Home assignment 2