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Simulation of some random processes
(the pictures are in postscript or pdf)

You can use these drawings if you want for your own publications : just, tell me !
If you desire a personal picture, you can also ask for it, but I don't promise anything....

CAUTION : some of the files are big (up to 4 Mo).
Wait a bit, it worths it  !!

Drawing of uniform quadrangulations (the map structure is lost, only the graph structure is kept (see Guillaume Chapuy's page for pictures where the "faces" are better represented).
Pictures in pdf :  size-150, size 2500, size 5000, size 7500, size 10000, size 20 000, size 25 000a,b,c,d,e,f,g , size 30 000, size 50 000
(size= number of vertices)

Drawing of uniform quadrangulations where the cycles that separate the maps have been deleted 
Pictures in pdf !!  size-150 000, size 150 000, size 300 000, size 400 000, size 500000
(size= number of vertices before deleting the separating cycles.)

Drawing of uniform planar trees
size = number of nodes, pictures in pdf,  size 50, size 100, size 500, size 1000, size 5000, size 15000

Some processes (the pictures are in postscript, drawn with gnuplot)

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 (killed the first time when it has 100 steps) 1
2
3
4
Uniform loop erased random walk (killed the first time when it has 1 000 steps) 1 2 3 4
Uniform loop erased random walk (killed the first time when it has 10 000 steps) 1 2 3 4
Uniform loop erased random walk (killed the first time when it has 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 the normalised 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 displacement distribution 5/(4(1+|x|)^7/2)

Brownian snake with lifetime the normalized Brownian excursion and R valued spatial process
Brownian snake with lifetime the normalized Brownian excursion and R^2 valued spatial process

Random walk in random environment (critical: site uniform on [0.3,0.7], random walk +-1)
(Each site s received a random variable x(s) , uniform in [a,b], independent from the other sites: the walk at site s goes up with proba x(s) and down with proba 1-x(s) )
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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