2 citations · 3 across the 8 of their papers we have counts for
13 papers
Monotonicity of escape probabilities for branching random walks on \Z^{d}
Achillefs Tzioufas
We study nearest-neighbors branching random walks started from a point at the interior of a hypercube. We show that the probability that the process escapes the hypercube is monoto…
No percolation at criticality
Achillefs Tzioufas
Ever since J.M. Hammersley showed the existence of phase-transitions regarding independent bond percolation on general dimensional integer-lattices in the late 50's, the…
The Several Dimensional Gambler's Ruin Problem
Achillefs Tzioufas
We consider the simple random walk on the -dimensional integer lattice from the perspective of evaluating asymptotically the duration of play in the multidimensional gambler\apo…
Percolation and Random Walks
Achillefs Tzioufas
The fourfold research proposal regards in particular: critical oriented percolation; random walk limit laws; neural networks with long-range connections; the ant in a labyrinth.
A note on spatial monotonicity for one-dimensional spin systems
Achillefs Tzioufas
We show that attractive, translation invariant, one-dimensional spin systems started from the unit step function possess the following basic property. At any time, the entire confi…
The randomly fluctuating hyperrectangles are spatially monotone
Achillefs Tzioufas
We show that the probability of a site being occupied at any instance of time in the one-dimensional randomly fluctuating hyperrectangles processes decreases monotonically with res…