Zobrazeno 1 - 10
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pro vyhledávání: '"Christopher D. Sinclair"'
Autor:
Christopher D. Sinclair
Publikováno v:
International Journal of Mathematics and Mathematical Sciences, Vol 2004, Iss 52, Pp 2773-2786 (2004)
We study the distribution of Mahler's measures of reciprocal polynomials with complex coefficients and bounded even degree. We discover that the distribution function associated to Mahler's measure restricted to monic reciprocal polynomials is a reci
Externí odkaz:
https://doaj.org/article/fd819c80f957420793f5ccfb4056eeb8
Publikováno v:
Communications in Mathematical Physics. 346:1051-1055
We correct an error in Theorem 12 of the original article concerning the edge scaling limit of the law of real eigenvalues for the real Ginibre ensemble.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::a1c4b749e1982896fa4f4636685a09ff
https://doi.org/10.1007/s00220-016-2703-y
https://doi.org/10.1007/s00220-016-2703-y
We consider the roots of uniformly chosen complex and real reciprocal polynomials of degree [Formula: see text] whose Mahler measure is bounded by a constant. After a change of variables, this reduces to a generalization of Ginibre’s complex and re
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c385eaea34f12f33a181dec851a70c76
http://arxiv.org/abs/1806.02914
http://arxiv.org/abs/1806.02914
Publikováno v:
Probability Theory and Related Fields. 155:127-164
We consider an ensemble of interacting charged particles on the line consisting of two species of particles with charge ratio 2 : 1 in the presence of the harmonic oscillator potential. The system is assumed to be at temperature corresponding to \bet
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e0bf6351377ab12dd006544f5450d38e
https://doi.org/10.1007/s00440-011-0394-z
https://doi.org/10.1007/s00440-011-0394-z
Publikováno v:
Communications in Mathematical Physics. 291:177-224
We give a closed form for the correlation functions of ensembles of a class of asymmetric real matrices in terms of the Pfaffian of an antisymmetric matrix formed from a $2 \times 2$ matrix kernel associated to the ensemble. We apply this result to t
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::7d235c7c95638caa62b6a7404842271d
https://doi.org/10.1007/s00220-009-0874-5
https://doi.org/10.1007/s00220-009-0874-5
Autor:
Christopher D. Sinclair
Publikováno v:
Journal of Statistical Physics. 136:17-33
Using the method of Tracy and Widom we rederive the correlation functions for \beta=1 Hermitian and real asymmetric ensembles of N x N matrices with N odd.
Comment: 15 pages
Comment: 15 pages
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::320a26be7042ff9da5bd03d5a12e8055
https://doi.org/10.1007/s10955-009-9771-8
https://doi.org/10.1007/s10955-009-9771-8
Publikováno v:
Journal de Théorie des Nombres de Bordeaux. 21:215-234
Etant donne un polynome f (x) ∈ ℤ[x], unitaire de degre N, et un entier positif l, on peut definir un nouveau polynome f l (x) ∈ ℤ[x], unitaire de degre N, en elevant chaque racine de f a la puissance l. Nous generalisons un lemme de Dobrowol
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::7920dbad697795e33d69963758950281
https://doi.org/10.5802/jtnb.667
https://doi.org/10.5802/jtnb.667
Autor:
Christopher D. Sinclair
Publikováno v:
Proceedings of the London Mathematical Society. 96:697-737
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::191df4911ef8bf11eb53cab35cc11407
https://doi.org/10.1112/plms/pdm037
https://doi.org/10.1112/plms/pdm037
The Mahler measure of a polynomial is a measure of complexity formed by taking the modulus of the leading coefficient times the modulus of the product of its roots outside the unit circle. The roots of a real degree $N$ polynomial chosen uniformly fr
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::53a785a140def9a7ec9e74f316570fe4
http://arxiv.org/abs/1307.4128
http://arxiv.org/abs/1307.4128
Autor:
Brian Rider, Christopher D. Sinclair
Publikováno v:
Ann. Appl. Probab. 24, no. 4 (2014), 1621-1651
The real Ginibre ensemble refers to the family of $n\times n$ matrices in which each entry is an independent Gaussian random variable of mean zero and variance one. Our main result is that the appropriately scaled spectral radius converges in law to
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e9be69e5f33a1c8d187835035cde167b
http://arxiv.org/abs/1209.6085
http://arxiv.org/abs/1209.6085