Moderate deviations and laws of the iterated logarithm for the renormalized self-intersection local times of planar random walks.

Bass, Richard F.; Chen, Xia; Rosen, Jay

Displaying similar documents to “Moderate deviations and laws of the iterated logarithm for the renormalized self-intersection local times of planar random walks.”

On the Poisson approximation of the binomial distribution.

Ruzankin, P.S. (2001)

Sibirskij Matematicheskij Zhurnal

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A study of the mean value of the error term in the mean square formula of the Riemann zeta-function in the critical strip $3 / 4 \leq σ < 1$

Yuk-Kam Lau (2006)

Journal de Théorie des Nombres de Bordeaux

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Let $E_{σ} (T)$ be the error term in the mean square formula of the Riemann zeta-function in the critical strip $1 / 2 < σ < 1$ . It is an analogue of the classical error term $E (T)$ . The research of $E (T)$ has a long history but the investigation of $E_{σ} (T)$ is quite new. In particular there is only a few information known about $E_{σ} (T)$ for $3 / 4 < σ < 1$ . As an exploration, we study its mean value $\int_{1}^{T} E_{σ} (u) d u$ . In this paper, we give it an Atkinson-type series expansion and explore many of its properties as a function of $T$ .

Lyapunov exponents for the parabolic Anderson model.

Cranston, M., Mountford, T.S., Shiga, T. (2002)

Acta Mathematica Universitatis Comenianae. New Series

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Enumeration of binary trees and universal types.

Knessl, Charles, Szpankowski, Wojciech (2005)

Discrete Mathematics and Theoretical Computer Science. DMTCS [electronic only]

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Ternary quadratic forms with rational zeros

John Friedlander, Henryk Iwaniec (2010)

Journal de Théorie des Nombres de Bordeaux

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We consider the Legendre quadratic forms $ϕ_{a b} (x, y, z) = a x^{2} + b y^{2} - z^{2}$ and, in particular, a question posed by J–P. Serre, to count the number of pairs of integers $1 \leq a \leq A, 1 \leq b \leq B$ , for which the form $ϕ_{a b}$ has a non-trivial rational zero. Under certain mild conditions on the integers $a, b$ , we are able to find the asymptotic formula for the number of such forms.