We present a method for obtaining upper bounds for the connective constant of selfavoiding walks. The method works for a large class of lattices, including all that have been studied in connectionâ€¦ (More)

LIMITED DISTRIBUTION NOTICE This report has been submitted for publication outside of IBM and will probably be copyrighted if accepted for publication. It has been issued as a Research Report forâ€¦ (More)

We study random graphs, both G(n, p) and G(n, m), with random orientations on the edges. For three fixed distinct vertices s, a, b we study the correlation, in the combined probability space, of theâ€¦ (More)

Consider a randomly oriented graph G = (V, E) and let a, s and b be three distinct vertices in V. We study the correlation between the events {a â†’ s} and {s â†’ b}. We show that, when G is the completeâ€¦ (More)

We present improved lower and upper bounds for the time constant of first-passage percolation on the square lattice. For the case of lower bounds, a new method, using the idea of a transition matrix,â€¦ (More)

First passage percolation on Z2 is a model for describing the spread of an infection on the sites of the square lattice. The infection is spread via nearest neighbor sites and the time dynamic isâ€¦ (More)

II Preface This is a Master's thesis written at the department of Mathematics at the Royal Institute of Technology (KTH) in Stockholm, supervised by Svante Linusson. It is assumed that the reader hasâ€¦ (More)

We study the random graph G(n, p) with a random orientation. For three fixed vertices s, a, b in G(n, p) we study the correlation of the events {a â†’ s} and {sâ†’ b}. We prove that asymptotically theâ€¦ (More)