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A stochastic process called Vertex-Reinforced Random Walk (VRRW) is defined in Pe-mantle (1988a). We consider this process in the case where the underlying graph is an infinite chain (i.e., the one-dimensional integer lattice). We show that the range is almost surely finite, that at least 5 points are visited infinitely often almost surely, and that with… (More)

We consider a Markov chain on a countable state space, on which is placed a random eld of traps, and ask whether the chain gets trapped almost surely. We show that the quenched problem (when the traps are xed) is equivalent to the annealed problem (when the traps are updated each unit of time) and give a criterion for almost sure trapping versus positive… (More)

In this paper we study a regular rooted coloured tree with random labels assigned to its edges, where the distribution of the label assigned to an edge depends on the colours of its endpoints. We obtain some new results relevant to this model and also show how our model generalizes many other probabilistic models, including random walk in random environment… (More)

We consider the following signaling game. Nature plays first from the set {1, 2}. Player 1 (the Sender) sees this and plays from the set {A, B}. Player 2 (the Receiver) sees only Player 1's play and plays from the set {1, 2}. Both players win if Player 2's play equals Nature's play and lose otherwise. Players are told whether they have won or lost, and the… (More)

- Henryk Fuks, Anna T. Lawniczak, Stanislav Volkov
- ACM Trans. Model. Comput. Simul.
- 2001

We investigate individual packet delay in a model of data networks with table-free, partial table and full table routing. We present analytical estimation for the average packet delay in a network with small partial routing table. Dependence of the delay on the size of the network and on the size of the partial routing table is examined numerically.… (More)

We consider a nearest-neighbor stochastic process on a rooted tree G which goes toward the root with probability 1 − ε when it visits a vertex for the first time. At all other times it behaves like a simple random walk on G. We show that for all ε ≥ 0 this process is transient. Also we consider a generalization of this process and establish its transience… (More)

We study the non-equilibrium dynamics of a one-dimensional interacting particle system that is a mixture of the voter model and exclusion process. With the process started from a finite perturbation of the ground-state Heaviside configuration consisting of 1s to the left of the origin and 0s elsewhere, we study the relaxation time τ , that is, the first… (More)

By a theorem of Volkov (2001) we know that on most graphs, with positive probability, the linearly vertex-reinforced random walk (VRRW) stays within a finite " trapping " subgraph at all large times. The question of whether this tail behavior occurs with probability one is open in general. R. Pemantle (1988) in his thesis proved, via a dynamical system… (More)

We study a one-dimensional random walk whose expected drift depends both on time and the position of a particle. We establish a non-trivial phase transition for the recurrence vs. transience of the walk, and show some interesting applications to Friedman's urn, as well as showing the connection with Lamperti's walk with asymptotically zero drift .

In this paper we study asymptotic behaviour of a growth process generated by a semi-deterministic variant of cooperative sequential adsorption model (CSA). This model can also be viewed as a particular queueing system with local interactions. We show that quite limited randomness of the model still generates a rich collection of possible limiting behaviours.