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The weak interlacing theorem enables us to bound the average number of leaves in a dense expander graph.. In this paper we proved a weak interlacing theorem for the
Hence, we can define the marked Gromov-weak topology based on weak convergence of marked distance matrix distributions, which turns ▼ I into a Polish space (Theorem
As a corollary we not only see that the image measure X(µ) is carried by the closure of the skeleton X(H) in the space J α,p , but that this is also true for the.. image measure
Let ψ and W be as described in the second part of the statement of the theorem and let φ denote the Laplace exponent of the descending ladder height subordinator associated to
At each time step, the mixer chooses a random vertex adjacent to its current position.. Then, with probability 1/2 it moves to that vertex, and with probability 1/2 it remains at
Our proof of Theorem 1.1 is based on estimates for the structure function, i.e., the spatial Fourier transform of the correlation function with respect to h·i , the
For a recurrent random walk in a random environment on a general locally finite connected graph, the mixing measure is unique if there exists a mixing measure Q which is supported
For the plane, sphere, and hyperbolic plane we consider the canonical invariant determinan- tal point processes Z ρ with intensity ρdν, where ν is the corresponding invariant
