Asymptotic windings of horocycles
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DOI: 10.1007/s11856-018-1761-6
Abstract: We analyze the scaling limits of the winding process for horocycles on noncompact hyperbolic surfaces with finite area. Initial conditions with precompact forward geodesics have scaling limits with gaussian and Cauchy components. Typical initial conditions… read more here.
Keywords: windings horocycles; scaling limits; asymptotic windings;
Scaling limits for a random boxes model
Sign Up to like & getrecommendations! Published in 2019 at "Advances in Applied Probability"
DOI: 10.1017/apr.2019.34
Abstract: Abstract We consider random rectangles in $\mathbb{R}^2$ that are distributed according to a Poisson random measure, i.e. independently and uniformly scattered in the plane. The distributions of the length and the width of the rectangles… read more here.
Keywords: boxes model; limits random; scaling limits; random boxes ... See more keywords
Scaling limits of anisotropic growth on logarithmic time-scales
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DOI: 10.1214/23-ejp964
Abstract: We study the anisotropic version of the Hastings-Levitov model AHL$(\nu)$. Previous results have shown that on bounded time-scales the harmonic measure on the boundary of the cluster converges, in the small-particle limit, to the solution… read more here.
Keywords: time; logarithmic time; time scales; harmonic measure ... See more keywords
Power scaling limits of diffraction-limited fiber amplifiers considering transverse mode instability.
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DOI: 10.1364/oe.483808
Abstract: An empirical TMI threshold formula is derived based on a recently developed model and used to analyze the power-scaling performance of ytterbium-doped silica glass and YAG (Y3Al5O12) and lutetia (Lu2O3) single-crystalline fiber amplifiers. Overall, the… read more here.
Keywords: diffraction limited; limits diffraction; power scaling; power ... See more keywords