Robert Parviainen

Estimation of bond percolation thresholds on the Archimedean lattices

We give accurate estimates for the bond percolation critical probabilities on seven Archimedean lattices, for which the critical probabilities are unknown, using an algorithm of Newman and Ziff.

Lower and Upper Bounds for the Time Constant of First-Passage Percolation

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, has been used. Numerical results for the exponential and uniform distributions are presented. A simulation study is included, which results in new estimates and improved upper confidence limits for the time constants.

Bounds for the connective constant of the hexagonal lattice

We give improved bounds for the connective constant of the hexagonal lattice. The lower bound is found by using Kestens method of irreducible bridges and by determining generating functions for br ...

Random Assignment with Integer Costs

The random assignment problem is to minimize the cost of an assignment in a n×n matrix of random costs. In this paper we study this problem for some integer valued cost distributions. We consider both uniform distributions on 1, 2, . . . , m, for m = n or n2, and random permutations of 1, 2, . . . , n for each row, or of 1, 2, . . . , n2 for the whole matrix. We find the limit of the expected cost for the “n2” cases, and prove bounds for the “n” cases. This is done by simple coupling arguments together with Aldous recent results for the continuous case. We also present a simulation study of these cases.