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Cube Root Fluctuations for the Corner Growth Model Associated to the Exclusion Process
We study the last-passage growth model on the planar integer lattice with exponential weights. With boundary conditions that represent the equilibrium exclusion process as seen from a particle right…
Second-order mean-field susceptible-infected-susceptible epidemic threshold.
Given the adjacency matrix A of a network, we present a second-order mean-field expansion that improves on the first-order N-intertwined susceptible-infected-susceptible (SIS) epidemic model.…
Susceptible-infected-susceptible epidemics on networks with general infection and cure times.
- E. Cator, R. van de Bovenkamp, P. Van Mieghem
- MathematicsPhysical review. E, Statistical, nonlinear, and…
- 24 June 2013
The GSIS model is extended to incorporate infection and curing or recovery times each characterized by a general distribution, and it is shown that the average number of infection attempts during a recovery time is the more natural key parameter, instead of the effective infection rate.
Epidemics in networks with nodal self-infection and the epidemic threshold.
An exact recursion relation for the Markov infinitesimal generator is presented and it is shown that for a certain range of small ε > 0, the in reality observed phase transition, also called the "metastable" state, that is characterized by the epidemic threshold is approximated.
Second class particles and cube root asymptotics for Hammersley's process
We show that, for a stationary version of Hammersley’s process, with Poisson sources on the positive x-axis and Poisson sinks on the positive y-axis, the variance of the length of a longest weakly…
Adaptivity and optimality of the monotone least-squares estimator
- E. Cator
- 13 May 2008
In this paper we will consider the estimation of a monotone regression (or density) function in a fixed point by the least squares (Grenander) estimator. We will show that this estimator is fully…
HAMMERSLEY'S PROCESS WITH SOURCES AND SINKS
We show that, for a stationary version of Hammersley’s process, with Poisson “sources” on the positive x-axis, and Poisson “sinks” on the positive y-axis, an isolated second-class particle, located…
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…
On the local fluctuations of last-passage percolation models
Susceptible-infected-susceptible epidemics on the complete graph and the star graph: exact analysis.
Two novel approaches are proposed: an ε-SIS generalized model and a modified SIS model that prevents the epidemic from dying out (i.e., without the complicating absorbing SIS state).