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Instead, we have to work a bit harder to establish ( 8 ) using uniform estimates on the classical Jacobi polynomials.. We assume here for simplicity that the polynomial F has
As pointed out in [2], an x-equilibrium stress exists if every interior edge lies on some x-monotone path, whose endpoints are boundary vertices.. Let us assume that we have
Stochastic fixed point equation, weighted branching process, infinite divisibility, L´evy measure, Choquet-Deny theorem, stable distributions.. AMS 2000
Keywords: Percolation, time constant, critical probabilities, Delaunay
Here the branching rate of the reactant process X ̺ is given by the additive functional of the collision local time of Brownian motion with (the catalyst) ̺ which is itself
On the particle level we may take the view of having a trivial spatial motion (particles are fixed inbetween the discrete branching points) and non-local branching, whereas
Generically, in our hierarchical model the migration process that sustains an equilibrium is at the border to recurrence in the case of one-level branching, and at the border to
To prove this theorem we extend the bounds proved in [ 2 ] for the continuous time simple random walk on (Γ , µ ) to the slightly more general random walks X and Y defined