The simple harmonic urn (2009)
Crane, Edward, Georgiou, Nicholas, Volkov, Stanislav, Wade, Andrew, Waters, Robert
We study a generalized Polya urn model with two types of ball. If the drawn ball is red it is replaced together with a black ball, but if the drawn ball is black it is replaced and a red ball is...
Forest fires on $\Z_+$ with ignition only at 0 (2009)
We consider a version of the forest fire model on graph $G$, where each vertex of a graph becomes occupied with rate one. A fixed vertex $v_0$ is hit by lightning with the same rate, and when this...
Queueing with neighbours (2009)
Shcherbakov, Vadim, Volkov, Stanislav
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...
Shcherbakov, Vadim, Volkov, Stanislav
In this paper we study stability of a growth process generated by a cooperative sequential adsorption model (CSA) on the lattice. The lattice CSA can be regarded as a variant of Polya urn scheme with...
VRRW on complete-like graphs: almost sure behavior (2009)
Limic, Vlada, Volkov, Stanislav
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....
Passage-time moments and hybrid zones for the exclusion-voter model (2008)
MacPhee, Iain M., Menshikov, Mikhail V., Volkov, Stanislav, Wade, Andrew R.
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...
Urn-related random walk with drift ρ xα / tβ (2008)
Menshikov, Mikhail; University Of Durham; Mikhail.Menshikov@durham.ac.uk@durham.ac.uk, Volkov, Stanislav; University Of Bristol; S.Volkov@bristol.ac.uk
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...
Robin Pemantle, Stanislav Volkov
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...
Robin Pemantle, Stanislav Volkov
A stochastic process called Vertex-Reinforced Random Walk (VRRW) is dened in Pemantle (1988a). We consider this process in the case where the underlying graph is an in nite chain (i.e., the...
A note on random walks in a hypercube (2007)
Volkov, Stanislav, Wong, Timothy
We study a simple random walk on an n-dimensional hypercube. For any starting position we find the probability of hitting vertex a before hitting vertex b, whenever a and b share the same edge. This...
Urn-related random walk with drift $\rho x^{\alpha} / t^{\beta}$ (2007)
Menshikov, Mikhail, Volkov, Stanislav
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...
Random environment on coloured trees (2007)
Menshikov, Mikhail, Petritis, Dimitri, Volkov, Stanislav
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...
Random environment on coloured trees (2007)
Menshikov, Mikhail, Petritis, Dimitri, Volkov, Stanislav
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...
Random environment on coloured trees (2007)
Menshikov, Mikhail, Petritis, Dimitri, Volkov, Stanislav
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...
A note on the lilypond model (2004)
Cotar, Codina, Volkov, Stanislav
We consider some generalizations of the germ-grain growing model studied by Daley, Mallows and Shepp (2000). In this model, a realization of a Poisson process on a line with points Xi is fixed. At...
Excited Random Walk on Trees (2003)
Volkov, Stanislav; University Of Bristol, UK; S.Volkov@bristol.ac.uk
We consider a nearest-neighbor stochastic process on a rooted tree $G$ which goes toward the root with probability $1-eps$ when it visits a vertex for the first time. At all other times it behaves...
Packet delay in models of data networks (2002)
Fuks, Henryk, Lawniczak, Anna T., Volkov, Stanislav
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...
Vertex-reinforced random walk on arbitrary graphs (2001)
Vertex-reinforced random walk (VRRW), defined by Pemantle, is a random process in a continuously changing environment which is more likely to visit states it has visited before. We consider VRRW on...
Loss of tension in an infinite membrane with holes distributed by Poisson law (1999)
Menshikov, Mikhail, Rybnikov, Konstantine, Volkov, Stanislav
If one randomly punches holes in an infinite tensed membrane, when does the tension cease to exist? This problem was introduced by R. Connelly in connection with applications of rigidity theory to...
Vertex-Reinforced Random Walk on Z Has Finite Range (1999)
Pemantle, Robin, Volkov, Stanislav
A stochastic process called vertex-reinforced random walk (VRRW) is defined in Pemantle [Ann. Probab. 16 1229–1241] . We consider this process in the case where the underlying graph is an infinite...
Vertex-reinforced random walk on Z has finite range (1999)
Robin Pemantle, Stanislav Volkov, Bernard Friedman's Urn
: A stochastic process called Vertex-Reinforced Random Walk (VRRW) is defined in Pemantle (1988a). We consider this process in the case where the underlying graph is an infinite chain (i.e., the...
Vertex-reinforced random walk on Z has finite range (1999)
Robin Pemantle, Stanislav Volkov, Bernard Friedman's Urn
: A stochastic process called Vertex-Reinforced Random Walk (VRRW) is defined in Pemantle (1988a). We consider this process in the case where the underlying graph is an infinite chain (i.e., the...
Markov Chains in a Field of Traps (1998)
Robin Pemantle, Stanislav Volkov
: We consider a Markov chain on a countable state space, on which is placed a random field of traps, and ask whether the chain gets trapped almost surely. We show that the quenched problem (when the...
Markov chains in a field of traps (1997)
Pemantle, Robin, Volkov, Stanislav
A general criterion is given for when a Markov chain trapped with probability p(x) in state x will be almost surely trapped. The quenched (state x is a trap forever with probability p(x)) and...
Vertex-reinfoced random walk on Z visits finitely many states (1997)
Pemantle, Robin, Volkov, Stanislav
Vertex-reinforced random walk is defined in Pemantle's (1988) thesis; it is a random walk that is biased to visit sites it has already visited a lot. We show that this reinforcement scheme, in...
A note on the simple random walk on : Probability of exiting sequences of sets
In this note we establish that the probability that the simple random walk on returns to its origin before leaving a strip of width L has asymptotically the same probability as the one for hitting...