276 citations · 4.5k across the 293 of their papers we have counts for
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Almost all orbits of the Collatz map attain almost bounded values
Terence Tao
Define the \emph{Collatz map} on the positive integers by setting equal to …
Random matrices: tail bounds for gaps between eigenvalues
Hoi Nguyen, Terence Tao, Van Vu
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 ra…
Random matrices have simple spectrum
Terence Tao, Van Vu
Let be a real symmetric random matrix in which the upper-triangular entries and diagonal entries are independent. We sho…
Local universality of zeroes of random polynomials
Terence Tao, Van Vu
In this paper, we establish some local universality results concerning the correlation functions of the zeroes of random polynomials with independent coefficients. More precisely,…
Random matrices: Universality of local spectral statistics of non-Hermitian matrices
Terence Tao, Van Vu
It is a result of Ginibre that the normalized bulk -point correlation functions of a complex Gaussian matrix with independent entries of mean zero and unit variance…
The asymptotic distribution of a single eigenvalue gap of a Wigner matrix
Terence Tao
We show that the distribution of (a suitable rescaling of) a single eigenvalue gap of a random Wigner matrix ensemble in the bulk is asymptotically given by…