scholarly journals Gap probabilities in the bulk of the Airy process

2021 ◽  
pp. 2250022
Author(s):  
Elliot Blackstone ◽  
Christophe Charlier ◽  
Jonatan Lenells
Keyword(s):  
Point Process ◽  
Airy Process ◽  
Airy Point Process ◽  
Gap Probabilities

We consider the probability that no points lie on [Formula: see text] large intervals in the bulk of the Airy point process. We make a conjecture for all the terms in the asymptotics up to and including the oscillations of order [Formula: see text], and we prove this conjecture for [Formula: see text].

scholarly journals Airy point process at the liquid-gas boundary

2018 ◽  
Vol 46 (5) ◽  
pp. 2973-3013 ◽  
Author(s):  
Vincent Beffara ◽  
Sunil Chhita ◽  
Kurt Johansson
Keyword(s):  
Point Process ◽  
Airy Point Process

scholarly journals Higher Order Large Gap Asymptotics at the Hard Edge for Muttalib–Borodin Ensembles

2021 ◽  
Author(s):  
Christophe Charlier ◽  
Jonatan Lenells ◽  
Julian Mauersberger
Keyword(s):  
Asymptotic Formula ◽  
Point Process ◽  
Bessel Functions ◽  
Hilbert Problem ◽  
Higher Order ◽  
Differential Identity ◽  
Hard Edge ◽  
Gap Probabilities ◽  
Riemann Hilbert Problem ◽  
Second Order Asymptotics

AbstractWe consider the limiting process that arises at the hard edge of Muttalib–Borodin ensembles. This point process depends on$$\theta > 0$$θ>0and has a kernel built out of Wright’s generalized Bessel functions. In a recent paper, Claeys, Girotti and Stivigny have established first and second order asymptotics for large gap probabilities in these ensembles. These asymptotics take the form$$\begin{aligned} {\mathbb {P}}(\text{ gap } \text{ on } [0,s]) = C \exp \left( -a s^{2\rho } + b s^{\rho } + c \ln s \right) (1 + o(1)) \qquad \text{ as } s \rightarrow + \infty , \end{aligned}$$P(gapon[0,s])=Cexp-as2ρ+bsρ+clns(1+o(1))ass→+∞,where the constants$$\rho $$ρ,a, andbhave been derived explicitly via a differential identity insand the analysis of a Riemann–Hilbert problem. Their method can be used to evaluatec(with more efforts), but does not allow for the evaluation ofC. In this work, we obtain expressions for the constantscandCby employing a differential identity in$$\theta $$θ. When$$\theta $$θis rational, we find thatCcan be expressed in terms of Barnes’G-function. We also show that the asymptotic formula can be extended to all orders ins.

Habitat use of toothed whales in a marine protected area based on point process models

2019 ◽  
Vol 609 ◽  
pp. 239-256 ◽  
Author(s):  
TL Silva ◽  
G Fay ◽  
TA Mooney ◽  
J Robbins ◽  
MT Weinrich ◽  
...  
Keyword(s):  
Habitat Use ◽  
Point Process ◽  
Protected Area ◽  
Marine Protected Area ◽  
Process Models ◽  
Point Process Models

On the generation and origin of I/f noise

1999 ◽  
Vol 4 ◽  
pp. 87-96 ◽  
Author(s):  
B. Kaulakys ◽  
T. Meškauskas
Keyword(s):  
Point Process ◽  
Solvable Model ◽  
Autoregressive Process ◽  
Wide Range ◽  
Occurrence Times

Simple analytically solvable model exhibiting 1/f spectrum in any desirably wide range of frequency is analysed. The model consists of pulses (point process) whose interevent times obey an autoregressive process with small damping. Analysis and generalizations of the model indicate to the possible origin of 1/f noise, i.e. random increments between the occurrence times of particles or pulses resulting in the clustering of the pulses.

Connected-Tube MPP Model for Unsupervised 3D Fiber Detection

2020 ◽  
Vol 2020 (14) ◽  
pp. 305-1-305-6
Author(s):  
Tianyu Li ◽  
Camilo G. Aguilar ◽  
Ronald F. Agyei ◽  
Imad A. Hanhan ◽  
Michael D. Sangid ◽  
...  
Keyword(s):  
Composite Material ◽  
Point Process ◽  
Marked Point ◽  
Experimental Results ◽  
Marked Point Process ◽  
Fiber Reinforced Composite ◽  
Reinforced Composite ◽  
Proposed Model ◽  
Cylinder Model ◽  
Reinforced Composite Material

In this paper, we extend our previous 2D connected-tube marked point process (MPP) model to a 3D connected-tube MPP model for fiber detection. In the 3D case, a tube is represented by a cylinder model with two spherical areas at its ends. The spherical area is used to define connection priors that encourage connection of tubes that belong to the same fiber. Since each long fiber can be fitted by a series of connected short tubes, the proposed model is capable of detecting curved long tubes. We present experimental results on fiber-reinforced composite material images to show the performance of our method.

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