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math.NT2025
Arithmetic sensitivity of cumulant growth in lacunary sums: transcendental versus algebraic ratio limits
Christoph Aistleitner, Zakhar Kabluchko, Joscha Prochno
We study the asymptotic behavior of cumulants of lacunary trigonometric sums , , and show that cumulant growth is highly sensitiv…
math.NT2025
A sharp threshold for arithmetic effects on the tail probabilities of lacunary sums
Christoph Aistleitner, Lorenz Fruehwirth, Joscha Prochno
A classical observation in analysis asserts that lacunary systems of dilated functions show many properties which are also typical for systems of independent random variables. For…