37 citations · 49 across the 2 of their papers we have counts for
5 papers
NoBLE for lattice trees and lattice animals
Robert Fitzner, Remco van der Hofstad
We study lattice trees (LTs) and animals (LAs) on the nearest-neighbor lattice in high dimensions. We prove that LTs and LAs display mean-field behavior above dimens…
Birds of a feather or opposites attract - effects in network modelling
Maria Deijfen, Robert Fitzner
We study properties of some standard network models when the population is split into two types and the connection pattern between the types is varied. The studied models are gener…
Mean-field behavior for nearest-neighbor percolation in
Robert Fitzner, Remco van der Hofstad
We prove that nearest-neighbor percolation in dimensions displays mean-field behavior by proving that the infrared bound holds, in turn implying the finiteness of the pe…
Generalized approach to the non-backtracking lace expansion
Robert Fitzner, Remco van der Hofstad
The lace expansion is a powerful perturbative technique to analyze the critical behavior of random spatial processes such as the self-avoiding walk, percolation and lattice trees a…
Non-backtracking random walk
Robert Fitzner, Remco van der Hofstad
We consider non-backtracking random walk (NBW) in the nearest-neighbor setting on the Zd-lattice and on tori. We evaluate the eigensystem of the m X m-dimensional transition matrix…