collatz conjecture 1dynamical systems 1logarithmic density 1probabilistic number theory 1random walks 1renewal processes 1
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math.PR2026
Almost all orbits of the Collatz map attain almost bounded values
Terence Tao
The paper proves that for any function f(N) that tends to infinity, the minimal value in the Collatz orbit of almost every positive integer (in logarithmic density) is at most f(N)…
math.PR2024
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…