Random matrices with independent ε-balanced entries in a log(n)^{1+δ} band—and arbitrary entries outside—have cokernels approaching the Cohen–Lenstra distribution; up to αn per column and βn per row bad entries are also tolerated.
and Venkatesh, Akshay and Westerland, Craig , TITLE =
5 Pith papers cite this work, alongside 110 external citations. Polarity classification is still indexing.
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Hub-and-spoke systems from symbolic dynamics can have completely positive mean dimension without uniformly positive mean dimension or entropy, with proofs linking entropy and mean dimension properties at the level of fixed covers.
Proves optimal homological vanishing line for H_i(B_n, V^{\otimes n}) giving power-saving cancellation bounds for Gauss sums and character sums over function fields, extending Patterson's conjecture.
Proves that sum of Steinhaus random multiplicative function over A converges to CN(0,1) only if |A|=o(N), with sharpness for most sets of density ρ where (1-ρ)^{-1}=o((log log N)^{1/2}).
Establishes group presentations for quotients of G_∅^T(K) in Γ-extensions and derives a random model predicting the distribution of these Galois groups over arbitrary global base fields Q.
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Universality for cokernels of partially random integral matrices
Random matrices with independent ε-balanced entries in a log(n)^{1+δ} band—and arbitrary entries outside—have cokernels approaching the Cohen–Lenstra distribution; up to αn per column and βn per row bad entries are also tolerated.
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Uniformly Positive Mean Dimension
Hub-and-spoke systems from symbolic dynamics can have completely positive mean dimension without uniformly positive mean dimension or entropy, with proofs linking entropy and mean dimension properties at the level of fixed covers.
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Optimal homological vanishing: cancellation of character sums and Patterson's conjecture over $\mathbb{F}_q[t]$
Proves optimal homological vanishing line for H_i(B_n, V^{\otimes n}) giving power-saving cancellation bounds for Gauss sums and character sums over function fields, extending Patterson's conjecture.
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Escaping Chaos in Random Multiplicative Functions
Proves that sum of Steinhaus random multiplicative function over A converges to CN(0,1) only if |A|=o(N), with sharpness for most sets of density ρ where (1-ρ)^{-1}=o((log log N)^{1/2}).
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Presentations of Galois groups of unramified extensions of global fields and its predicted distribution
Establishes group presentations for quotients of G_∅^T(K) in Γ-extensions and derives a random model predicting the distribution of these Galois groups over arbitrary global base fields Q.