getdoc807c. 87KB Jun 04 2011 12:04:35 AM
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Limit points for the positive eigenvalues of the normalized Laplacian matrix of a graph are considered.Specifically, it is shown that the set of limit points for the j -th smallest
The notion of weak uniqueness requiring that the joint distribution of the solution and the stochastic inputs be uniquely determined used by Engelbert and also by Jacod (12) is
We determine exactly when a certain randomly weighted self–normalized sum converges in distribution, partially verifying a 1965 conjecture of Leo Breiman, and then apply our results
In the dependent case, the limit N may not be a Poisson process, but belongs to the class of infinitely divisible point processes (under generally weak assumptions).. This
We prove a non-standard functional limit theorem for a two dimensional simple random walk on some randomly oriented lattices.. This random walk, already known to be transient, has
For a much-studied model of random copolymer at a selective interface we prove that the slope of the critical curve in the weak-disorder limit is strictly smaller than 1, which is
In the second example, although the family of conditioned laws are tight in the Martin topology, they possess multiple limit points so that weak convergence fails altogether..
If instead of number of vertices we define “large” in terms of, say, diameter or volume of the convex hull, then these questions can be answered for subcritical percolation using
