A Function Arising in One-Dimensional Percolation (M. L. Glasser)

On a PDE Arising in One-Dimensional Stochastic Control Problems

The paper provides a systematic way for finding a partial differential equation that directly characterizes the optimal control, in the framework of one–dimensional stochastic control problems of Mayer type, with no constraints on the controls. The results obtained are applied to continuous–time portfolio problems.

On percolation in one-dimensional stable Poisson graphs

Equip each point x of a homogeneous Poisson point process P onR withDx edge stubs, where theDx are i.i.d. positive integer-valued random variables with distribution given by μ. Following the stable multi-matching scheme introduced by Deijfen, Häggström and Holroyd [1], we pair off edge stubs in a series of rounds to form the edge set of a graph G on the vertex set P. In this note, we answer que...

Exact Determination of the Two-Point Cluster Function for One-Dimensional Continuum Percolation

The two-point cluster function C2(rl, r2) provides a measure of clustering in continuum models of disordered many-particle systems and thus is a useful signature of the microstructure. For a two-phase disordered medium, C2(rt, r2) is defined to be the probability of finding two points at positions r t and r_, in the same cluster o f one o f the phases. An exact ana/ytical expression is found fo...

One dimensional infinite-horizon variational problems arising in viscoelasticity

Directed Percolation arising in Stochastic Cellular Automata

Cellular automata are both seen as a model of computation and as tools to model real life systems. Historically they were studied under synchronous dynamics where all the cells of the system are updated at each time step. Meanwhile the question of probabilistic dynamics emerges: on the one hand, to develop cellular automata which are capable of reliable computation even when some random errors ...