scholarly journals The Width of Galton-Watson Trees Conditioned by the Size

2004 ◽  
Vol Vol. 6 no. 2 ◽  
Author(s):  
Michael Drmota ◽  
Bernhard Gittenberger
Keyword(s):  
Limit Theorem ◽  
Local Time ◽  
Weak Limit ◽  
Brownian Excursion ◽  
International Audience ◽  
Weak Limit Theorem

International audience It is proved that the moments of the width of Galton-Watson trees of size n and with offspring variance σ ^2 are asymptotically given by (σ √n)^pm_p where m_p are the moments of the maximum of the local time of a standard scaled Brownian excursion. This is done by combining a weak limit theorem and a tightness estimate. The method is quite general and we state some further applications.

scholarly journals A Weak Limit Theorem for Generalized Jiřina Processes

2009 ◽  
Vol 46 (2) ◽  
pp. 453-462 ◽  
Author(s):  
Yuqiang Li
Keyword(s):  
Limit Theorem ◽  
Diffusion Process ◽  
Nonlinear Diffusion ◽  
Weak Limit ◽  
Weak Limit Theorem ◽  
Lévy Jumps

In this paper we prove that a sequence of scaled generalized Jiřina processes can converge weakly to a nonlinear diffusion process with Lévy jumps under certain conditions.

scholarly journals The profile of unlabeled trees

2005 ◽  
Vol DMTCS Proceedings vol. AD,... (Proceedings) ◽  
Author(s):  
Bernhard Gittenberger
Keyword(s):  
Local Time ◽  
Joint Distribution ◽  
Random Trees ◽  
Rooted Trees ◽  
Brownian Excursion ◽  
Level Number ◽  
International Audience ◽  
The Times ◽  
Simply Generated Trees

International audience We consider the number of nodes in the levels of unlabeled rooted random trees and show that the joint distribution of several level sizes (where the level number is scaled by $\sqrt{n}$) weakly converges to the distribution of the local time of a Brownian excursion evaluated at the times corresponding to the level numbers. This extends existing results for simply generated trees and forests to the case of unlabeled rooted trees.

scholarly journals Weak limit theorem for a nonlinear quantum walk

2018 ◽  
Vol 17 (9) ◽  
Author(s):  
Masaya Maeda ◽  
Hironobu Sasaki ◽  
Etsuo Segawa ◽  
Akito Suzuki ◽  
Kanako Suzuki
Keyword(s):  
Limit Theorem ◽  
Quantum Walk ◽  
Weak Limit ◽  
Nonlinear Quantum ◽  
Weak Limit Theorem

The Brownian excursion multi-dimensional local time density

1999 ◽  
Vol 36 (2) ◽  
pp. 350-373 ◽  
Author(s):  
Bernhard Gittenberger ◽  
Guy Louchard
Keyword(s):  
Limit Theorem ◽  
Local Time ◽  
Direct Method ◽  
Brownian Excursion ◽  
A Direct Method ◽  
Time Density

Expressions for the multi-dimensional densities of Brownian excursion local time are derived by two different methods: a direct method based on Kac's formula for Brownian functionals and an indirect one based on a limit theorem for Galton–Watson trees.

scholarly journals A Weak Limit Theorem for Generalized Jiřina Processes

2009 ◽  
Vol 46 (02) ◽  
pp. 453-462 ◽  
Author(s):  
Yuqiang Li
Keyword(s):  
Limit Theorem ◽  
Diffusion Process ◽  
Nonlinear Diffusion ◽  
Weak Limit ◽  
Weak Limit Theorem ◽  
Lévy Jumps

In this paper we prove that a sequence of scaled generalized Jiřina processes can converge weakly to a nonlinear diffusion process with Lévy jumps under certain conditions.

scholarly journals AN ALGEBRAIC STRUCTURE FOR ONE-DIMENSIONAL QUANTUM WALKS AND A NEW PROOF OF THE WEAK LIMIT THEOREM

2013 ◽  
Vol 16 (02) ◽  
pp. 1350018
Author(s):  
TATSUYA TATE
Keyword(s):  
Limit Theorem ◽  
Characteristic Function ◽  
Algebraic Structure ◽  
Chebyshev Polynomials ◽  
Transition Probability ◽  
Weak Limit ◽  
Quantum Walks ◽  
One Dimensional ◽  
Natural Computation ◽  
Weak Limit Theorem

An algebraic structure for one-dimensional quantum walks is introduced. This structure characterizes, in some sense, one-dimensional quantum walks. A natural computation using this algebraic structure leads us to obtain an effective formula for the characteristic function of the transition probability. Then, the weak limit theorem for the transition probability of quantum walks is deduced by using simple properties of the Chebyshev polynomials.

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