Collisions among random walks on a graph
SIAM Journal on Discrete Mathematics
Compatible sequences and a slow Winkler percolation
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Clairvoyant scheduling of random walks
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Evasive random walks and the clairvoyant demon
Random Structures & Algorithms
Compatible Sequences and a Slow Winkler Percolation
Combinatorics, Probability and Computing
On a form of coordinate percolation
Combinatorics, Probability and Computing
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Consider the integer lattice L = ℤ2. For some m ≥ 4, let us colour each column of this lattice independently and uniformly with one of m colours. We do the same for the rows, independently of the columns. A point of L will be called blocked if its row and column have the same colour. We say that this random configuration percolates if there is a path in L starting at the origin, consisting of rightward and upward unit steps, avoiding the blocked points. As a problem arising in distributed computing, it has been conjectured that for m ≥ 4 the configuration percolates with positive probability. This question remains open, but we prove that the probability that there is percolation to distance n but not to infinity is not exponentially small in n. This narrows the range of methods available for proving the conjecture.