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We study the global fluctuations for linear statistics of the form n i=1 f (λ i) as n → ∞, for C 1 functions f , and λ 1 ,. .. , λn being the eigenvalues of a (general) β-Jacobi ensemble [18, 29]. The fluctuation from the mean (n i=1 f (λ i) − E n i=1 f (λ i)) is given asymptotically by a Gaussian process. We compute the covariance matrix for the process… (More)

- Elliot Paquette, Kalamazoo College, Christopher Seaton
- 2008

A Poincaré-Hopf theorem in the spirit of Pugh is proven for compact orbifolds with boundary. The theorem relates the index sum of a smooth vector field in generic contact with the boundary orbifold to the Euler-Satake characteristic of the orbifold and a boundary term. The boundary term is expressed as a sum of Euler characteristics of tangency and… (More)

- Abor Cs´ardi, Péterérdi, D Sc, Henry R Luce, Daniel Catlin, Andrew Schneider +2 others
- 2007

It is that the sciences do not try to explain, they hardly even try to interpret, they mainly make models. By a model is meant a mathematical construct which, with the addition of certain verbal interpretations, describes observed phenomena. The justification of such a mathematical construct is solely and precisely that it is expected to work—that is,… (More)

- Elliot Paquette
- 2014

We prove almost sure convergence of the maximum degree in an evolving tree model combining local choice and preferential attachment. At each step in the growth of the graph, a new vertex is introduced. A fixed, finite number of possible neighbors are sampled from the existing vertices with probability proportional to degree. Of these possibilities, the new… (More)

We consider the regularization of matrices M N written in Jordan form by additive Gaussian noise N −γ G N , where G N is a matrix of i.i.d. standard Gaussians and γ > 1 /2 so that the operator norm of the additive noise tends to 0 with N. Under mild conditions on the structure of M N we evaluate the limit of the empirical measure of eigenvalues of M N + N… (More)

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