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Nevertheless, these results are strong enough to be able to determine the inertia set of each graph on 6 or fewer vertices and can be applied to many graphs with larger order as
The asymptotics of the Schatten norms of finite Toeplitz matrices generated by functions with a Fisher-Hartwig singularity are described as the matrix dimension n goes to infinity..
Consider, for instance, the crossing probability of a square in (ordinary) two-dimensional Bernoulli percolation in the scaling limit (i.e., as the lattice spacing goes to zero)
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
One example of a graph model for obtaining a prescribed degree distribution is the so called configuration model – see Molloy and Reed (1995,1998) – where, given n vertices, each
In Section 6 we prove Theorem 3.2 about the convergence of the renormalization branching process to a time-homogeneous limit.. In Section 7 , we prove the statements from
Submitted to EJP on June 19, 2000.. In probabilistic terms the associated process X can be obtained by a time change of X. For the moment we will just discuss the case K = [0, 1],
If | N | = p, then by Proposition 2.1, the quotient graph XN of X corre- sponding to the orbits of N is a connected cubic symmetric graph of order 12, which is impossible by [2]..
