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Simulations of some random processes
(the pictures are in postscript)


You can use this drawings if you want for your own publications.

Brownian motion 1 2 3
Brownian motion in R^2 1 2 3 4
Brownian bridge 1 2 3 4
Brownian excursion 1 2 3 4
Brownian meander 1 1 3 4
Uniform loop erased random walk (100 steps) 1
2
3
4
Uniform loop erased random walk (1 000 steps) 1 2 3 4
Uniform loop erased random walk (10 000 steps) 1 2 3 4
Uniform loop erased random walk (100000 steps) 1 2
3
4
Uniform spanning tree: grid 50 x 50
1
2
3
Uniform spanning tree: grid 100 x 100 1
2
3
Uniform spanning tree: grid 200 x 200 1
2
3

Bessel processes with parameter
2 3 20 100 1000

Local time at time 1 of Brownian motion
Local time at time 1 of Brownian bridge
Local time at time 1 of Brownian excursion

Discrete branching random walk (size 58 000) with positive mean displacment (and finite variance)
Discrete branching random walk (size 58 000) with 0 mean displacment and gaussian displacments.
Discrete branching random walk (size 58 000) with cauchy displacments
Discrete branching random walk (size 180 000) with displacment distribution 5/(4(1+|x|)^7/2)

Brownian snake (with lifetime the normalized Brownian excursion) in R
Brownian snake (with lifetime the normalized Brownian excursion) in R2

Random walk in random environment (critical: site uniform on [0.3,0.7], random walk +-1)
Random walk in random environment (critical: site uniform on [0.2,0.8], random walk +-1)
Random walk in random environment (site uniform on [0.2,0.9])



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