E-mail: math at fitzner.nl
Eindhoven University of Technology,
Department of Mathematics & Computer Science,
P.O. Box 513, 5600 MB Eindhoven,
Most of my research is in the field of statistical physics. During my time in Stockholm I also worked on models for the the spread of information/diseases in networks.
Up to now my main scientific contribution is establish my PhD thesis:
Remco van der Hofstad and I modify a perturbation technique known as the lace expansion to enhance results in the nearest-neighbor setting. We show mean-field behavior for self-avoiding walk, lattice trees, lattice animals and percolation on the nearest-neighbor Zd-lattice in high dimensions. The aim thereby is to prove mean-field results above, but close to, their upper critical dimensions and verify for which dimension we can apply technique.
In the table below we state in which dimension we succeed to prove mean-field behavior using the techniques derived in my thesis.
proven in literatur
we prove it for
The proof of these results require a computer-assisted proof, whose implementation can be found here.
As a side project I developed a program that can simulate several models of random media, like random walks and percolation. If you have installed java on your system you can load it as an applet. Click on the image to go to the page of the program.
You can also download to the program and save simulated models directly into a file. Everyone is invited to use the program and the generated pictures for talks, research and teaching.