New Approaches to Modern Physics/DIRECTED PERCOLATION


118093 - New Approaches to Modern Physics
WINTER 2005

Advanced Statistical Mechanics


[Course Summary][Links to Lecture Notes and Homework][Announcements] [For Lecturers]
[JOAN ADLER's lectures]

DIRECTED PERCOLATION

  1. This seems a trivial change but because of alteration of basic symmetry it is one of the few percolation variants that really give different critical exponents.

  2. There is as yet no explicit solution, but there are many rigorous results and the various quantities are extremely well behaved. I personally believe it is solvable.

  3. Reggeon Field Theory falls in the same universality class.

  4. Lets orient the square lattice in directions north, south, east and west. if the ant of the previous topic can only walk north and east and never south or west it would be more difficult to find a connected path. The critical exponents would also change.

  5. There are immediate applications to percolation of forest fires in a wind.

  6. A beautiful application of directed percolation to galaxy formation is in the project of Liron Glezer.