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While Chan and Li’s proof of Horn’s Theorem and our proof of Mirsky’s Theorem have a similar structure, there is a significant difference: The matrices whose existence is guaranteed
The main objective in this section is to prove the following theorem concerning the conditional distribution of the number of edges given the colouring..
(Actually, Watanabe’s proof of Hawkes’s conjecture is a consequence of Theorem 1.2 [ 21 ].. that provides a general criterion to decide whether the branching measure is an
Proof : The only problem is to prove formula (4), that is to prove that u is the sum of its Taylor expansion with respect to λ. In the case where A is a complex Banach algebra,
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
The extension of sublinearity on average to pointwise sublinearity is the main novel part of the proof which, unfortunately, still makes non-trivial use of the “heat-kernel
We introduce a simple tree growth process that gives rise to a new two-parameter family of discrete fragmentation trees that extends Ford’s alpha model to multifurcating trees
We present a short probabilistic proof of a weak convergence result for the number of cuts needed to isolate the root of a random recursive tree.. The proof is based on a
