1
Introduction
2
Grid Paths and Last Passage Percolation
▶
2.1
Basic Definitions
3
Gumbel and Exponential Distributions
▶
3.1
The Gumbel Distribution
3.2
Transformation to Exponential Distribution
4
The Coupling Construction
▶
4.1
Approximate Gumbel Distribution
4.2
The Coupling Function
4.3
LPP Definitions
5
Perturbation Analysis
▶
5.1
Coupling Bounds
6
Convergence Properties
▶
6.1
Convergence Definitions
6.2
Known Results (Axiomatized)
6.3
Slutsky’s Theorem
6.4
Auxiliary Convergence Lemmas
7
Main Theorem
Dependency graph
Approximate Gumbel Last Passage Percolation
James Stephens
1
Introduction
2
Grid Paths and Last Passage Percolation
2.1
Basic Definitions
3
Gumbel and Exponential Distributions
3.1
The Gumbel Distribution
3.2
Transformation to Exponential Distribution
4
The Coupling Construction
4.1
Approximate Gumbel Distribution
4.2
The Coupling Function
4.3
LPP Definitions
5
Perturbation Analysis
5.1
Coupling Bounds
6
Convergence Properties
6.1
Convergence Definitions
6.2
Known Results (Axiomatized)
6.3
Slutsky’s Theorem
6.4
Auxiliary Convergence Lemmas
7
Main Theorem