W1,+-interpolation of probability measures on graphs

COSPECTRALITY MEASURES OF GRAPHS WITH AT MOST SIX VERTICES

Cospectrality of two graphs measures the differences between the ordered spectrum of these graphs in various ways. Actually, the origin of this concept came back to Richard Brualdi's problems that are proposed in cite{braldi}: Let $G_n$ and $G'_n$ be two nonisomorphic simple graphs on $n$ vertices with spectra$$lambda_1 geq lambda_2 geq cdots geq lambda_n ;;;text{and};;; lambda'_1 geq lambda'_2...

A Note on the Localization Number of Random Graphs: Diameter Two Case

We study the localization game on dense random graphs. In this game, a cop x tries to locate a robber y by asking for the graph distance of y from every vertex in a sequence of sets W1,W2, . . . ,W`. We prove high probability upper and lower bounds for the minimum size of each Wi that will guarantee that x will be able to locate y.

The Interpolation Method for Random Graphs with Prescribed Degrees

Errata to Processes on Unimodular Random Networks

The statement in the introduction, “Unimodularity of a probability measure μ on rooted graphs is equivalent to the property that a reversible stationary distribution for this chain is given by the root-degree biasing of μ . . . ”, is incorrect. Unimodularity implies this reversibility, but is not implied by it. There is a similar loss of precision at the beginning of Section 4. The correct stat...

Nevanlinna-pick Interpolation for C + Bh ∞

In this paper we will consider the Nevanlinna-Pick problem for a class of subalgebras of H∞. Let us assume that we are given n points z1, . . . , zn ∈ D, n complex numbers w1, . . . , wn and a subalgebra A of H ∞. We will say that a function f ∈ A, interpolates the values z1, . . . , zn to w1, . . . , wn if and only if ‖f‖∞ ≤ 1 and f(zj) = wj . Such an f will be called an interpolating function...