12 Result(s)
within
Terence Tao
Theoretical, Mathematical and Computational Physics
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Article
Sums of GUE matrices and concentration of hives from correlation decay of eigengaps
Associated to two given sequences of eigenvalues \(\lambda _1 \ge \cdots \ge \lambda _n\) ...
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Random matrices: tail bounds for gaps between eigenvalues
Gaps (or spacings) between consecutive eigenvalues are a central topic in random matrix theory. The goal of this paper is to study the tail distribution of these gaps in various random matrix models. We give t...
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A multi-dimensional Szemerédi theorem for the primes via a correspondence principle
We establish a version of the Furstenberg-Katznelson multi-dimensional Szemerédi theorem in the primes P:= {2, 3, 5, …}, which roughly speaking asserts that any dense subset of P ...
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Article
Effective Limiting Absorption Principles, and Applications
The limiting absorption principle asserts that if H is a suitable Schrödinger operator, and f lives in a suitable weighted L 2 space (namely \({H^{0, 1/2 + \sigma}}\) ...
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Erratum to: Outliers in the spectrum of iid matrices with bounded rank perturbations
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The asymptotic distribution of a single eigenvalue gap of a Wigner matrix
We show that the distribution of (a suitable rescaling of) a single eigenvalue gap \(\lambda _{i+1}(M_n)-\lambda _i(M_n)\) of a...
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Outliers in the spectrum of iid matrices with bounded rank perturbations
It is known that if one perturbs a large iid random matrix by a bounded rank error, then the majority of the eigenvalues will remain distributed according to the circular law. However, the bounded rank perturb...
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Scale-oblivious metric fragmentation and the nonlinear Dvoretzky theorem
We introduce a randomized iterative fragmentation procedure for finite metric spaces, which is guaranteed to result in a polynomially large subset that is D-equivalent to an ultrametric, where D ∈ (2,∞) is a pres...
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Strongly dense free subgroups of semisimple algebraic groups
We show that (with one possible exception) there exist strongly dense free subgroups in any semisimple algebraic group over a large enough field. These are nonabelian free subgroups all of whose subgroups are ...
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Open AccessRandom Matrices: Universality of Local Eigenvalue Statistics up to the Edge
This is a continuation of our earlier paper (Tao and Vu, http://arxiv.org/abs/0908.1982v4[math.PR], 2010) on the universality of the eigenvalues of Wigner ra...
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Global Regularity for the Maxwell-Klein-Gordon Equation with Small Critical Sobolev Norm in High Dimensions
We show that in dimensions n ≥ 6 one has global regularity for the Maxwell-Klein-Gordon equations in the Coulomb gauge provided that the critical Sobolev norm of the initial d...
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Global Regularity of Wave Maps¶II. Small Energy in Two Dimensions
We show that wave maps from Minkowski space ℝ1+ n to a sphere S m ...
