Elliot Paquette

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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)
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)
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)
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