KTH/SU Mathematics Colloquium
May 6, 2009
Balint Toth, TU Budapest
Random walks with long memory
Ordinary (e.g. simple symmetric) random walk models inter alia
physical diffusion in particle systems. It is well known that under
diffusive scaling (that is: scaling space with square root of time)
simple symmetric random walk converges weakly to (mathematical)
Brownian motion. However, in truly interacting physical systems
displacements of diffusing particles do *not* arise as sums of
essentially independent steps and this causes relevant long range
dependencies which could lead to dramatic consequences in the scaling
behaviour. In my talk I will survey some natural examples of random
walks and diffusions with long memory which in low dimension (d=1,2)
show anomalous scaling and in high dimension (d=3,4,...) behave
robustly, like ordinary random walk.