scholarly journals Joint distribution of Busemann functions in the exactly solvable corner growth model

2020 ◽  
Vol 1 (1) ◽  
pp. 55-100
Author(s):  
Wai-Tong (Louis) Fan ◽  
Timo Seppäläinen
Keyword(s):  
Growth Model ◽  
Joint Distribution ◽  
Exactly Solvable ◽  
Busemann Functions ◽  
Corner Growth Model

scholarly journals Stationary cocycles and Busemann functions for the corner growth model

2016 ◽  
Vol 169 (1-2) ◽  
pp. 177-222 ◽  
Author(s):  
Nicos Georgiou ◽  
Firas Rassoul-Agha ◽  
Timo Seppäläinen
Keyword(s):  
Growth Model ◽  
Busemann Functions ◽  
Corner Growth Model

scholarly journals Non-existence of bi-infinite geodesics in the exponential corner growth model

2020 ◽  
Vol 8 ◽  
Author(s):  
Márton Balázs ◽  
Ofer Busani ◽  
Timo Seppäläinen
Keyword(s):  
Growth Model ◽  
Coarse Graining ◽  
Exponential Weights ◽  
Percolation Process ◽  
Last Passage Percolation ◽  
Corner Growth Model ◽  
And Control

Abstract This paper gives a self-contained proof of the non-existence of nontrivial bi-infinite geodesics in directed planar last-passage percolation with exponential weights. The techniques used are couplings, coarse graining, and control of geodesics through planarity and estimates derived from increment-stationary versions of the last-passage percolation process.

Inferring the Distribution of the Parameters of the von Bertalanffy Growth Model from Length Moments

1988 ◽  
Vol 45 (10) ◽  
pp. 1779-1788 ◽  
Author(s):  
Robert L. Burr
Keyword(s):  
Growth Model ◽  
Joint Distribution ◽  
Probability Distributions ◽  
Joint Probability ◽  
Future Research ◽  
Parameter Estimates ◽  
Von Bertalanffy ◽  
Animal Populations ◽  
Von Bertalanffy Growth Model ◽  
Joint Probability Distributions

A theoretical approach is described for determining the joint distribution of the parameters of the von Bertalanffy growth model from statistical moments of length. The approach extends the work of K. J. Sainsbury, who had demonstrated that different mean parameter estimates are obtained by assuming that the von Bertalanffy equation applies to individual fish rather than to groups of fish. Sainsbury articulated the goal of studying the joint probability distributions of K and L∞ in animal populations and developed a maximum likelihood procedure for estimating the parameters of particular distributional forms describing K and L∞, which were assumed for mathematical convenience to be statistically independent. The primary goal of the present paper is to provide a framework for future research in generalizing Sainsbury's approach by considering (K, L∞) to be a random vector described by a joint probability density function and by allowing broader classes of distributions to be considered. Minimum cross-entropy (MCE) inversion, an information–theoretic methodology for approximating probability distributions, is shown to be effective in selecting a reasonable and unique joint distribution corresponding to observable length moments. Appealing features of the MCE methodology include the ability to include prior knowledge of uncertain applicability and the capacity of the resulting approximate distribution to represent potential stochastic dependencies between the von Bertalanffy parameters. Several numerical examples, using simulated and historical data, are presented to illustrate how information about the variation and covariation of L∞ and K can be inferred from a minimal set of length moments. The directions developed in this paper are far from a practical and useful methodology. The MCE inversion procedure is a "method of moments," with no statistical assessment of reliability. Further research is needed to make this promising pdf approximation scheme better suited for real fisheries problems.

scholarly journals Non-existence of bi-infinite geodesics in the exponential corner growth model – Corrigendum

2021 ◽  
Vol 9 ◽  
Author(s):  
Márton Balázs ◽  
Ofer Busani ◽  
Timo Seppäläinen
Keyword(s):  
Growth Model ◽  
Corner Growth Model

scholarly journals Flats, spikes and crevices: the evolving shape of the inhomogeneous corner growth model

2021 ◽  
Vol 26 (none) ◽  
Author(s):  
Elnur Emrah ◽  
Christopher Janjigian ◽  
Timo Seppäläinen
Keyword(s):  
Growth Model ◽  
Corner Growth Model

scholarly journals Cube Root Fluctuations for the Corner Growth Model Associated to the Exclusion Process

2006 ◽  
Vol 11 (0) ◽  
pp. 1094-1132 ◽  
Author(s):  
Marton Balazs ◽  
Eric Cator ◽  
Timo Seppalainen
Keyword(s):  
Growth Model ◽  
Exclusion Process ◽  
Cube Root ◽  
Corner Growth Model

scholarly journals Geodesics and the competition interface for the corner growth model

2016 ◽  
Vol 169 (1-2) ◽  
pp. 223-255 ◽  
Author(s):  
Nicos Georgiou ◽  
Firas Rassoul-Agha ◽  
Timo Seppäläinen
Keyword(s):  
Growth Model ◽  
Corner Growth Model ◽  
Competition Interface
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