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Local Behaviour of Airy Processes
The Airy processes describe limit fluctuations in a wide range of growth models, where each particular Airy process depends on the geometry of the initial profile. We show how the coupling method,…
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On the local fluctuations of last-passage percolation models
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A phase transition for competition interfaces
We study the competition interface between two growing clusters in a growth model associated to last-passage percolation. When the initial unoccupied set is approximately a cone, we show that this…
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Busemann functions and the speed of a second class particle in the rarefaction fan
In this paper we will show how the results found in [Probab. Theory Related Fields 154 (2012) 89–125], about the Busemann functions in last-passage percolation, can be used to calculate the…
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Duality between coalescence times and exit points in last-passage percolation models
In this paper we prove a duality relation between coalescence times and exit points in last-passage percolation models with exponential weights. As a consequence, we get lower bounds for coalescence…
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Busemann functions and equilibrium measures in last passage percolation models
The interplay between two-dimensional percolation growth models and one-dimensional particle processes has been a fruitful source of interesting mathematical phenomena. In this paper we develop a…
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Multitype shape theorems for first passage percolation models
A Euclidean first passage percolation model describing the competing growth between k different types of infection is considered. We focus on the long-time behavior of this multitype growth process…
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Local Behavior of Airy Processes
The Airy processes describe spatial fluctuations in wide range of growth models, where each particular Airy process arising in each case depends on the geometry of the initial profile. We show how…
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Tightness for the interface of the one-dimensional contact process
We consider a symmetric, finite-range contact process with two types of infection; both have the same (supercritical) infection rate and heal at rate 1, but sites infected by Infection 1 are immune…
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Asymptotics for First-Passage Times on Delaunay Triangulations
TLDR
This paper shows a sufficient condition to ensure that μ>0 and derive some upper bounds for fluctuations and proofs are based on percolation ideas and on the method of martingales with bounded increments.
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