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We prove that the variance of the current across a characteristic is of order t in a stationary constant rate totally asymmetric zero range process, and that the diffusivity has order t. This is a step towards proving universality of this scaling behavior in the class of one-dimensional interacting systems with one conserved quantity and concave… (More)

- David F. Gleich, Júlia Komjáthy, +6 authors Gerhard Weikum
- 2015

We study robustness under random attack for a class of networks, in which new nodes are given a spatial position and connect to existing vertices with a probability favouring short spatial distances and high degrees. In this model of a scale-free network with clustering one can independently tune the power law exponent τ > 2 of the degree distribution and a… (More)

Suppose that G and H are finite, connected graphs, G regular, X is a lazy random walk on G and Z is a reversible ergodic Markov chain on H. The generalized lamplighter chain X associated with X and Z is the random walk on the wreath product H o G, the graph whose vertices consist of pairs (f, x) where f = (fv)v∈V (G) is a labeling of the vertices of G by… (More)

We prove that the variance of the current across a characteristic is of order t in a stationary constant rate totally asymmetric zero range process, and that the diffusivity has order t. This is a step towards proving universality of this scaling behavior in the class of one-dimensional interacting systems with one conserved quantity and concave… (More)

This review article discusses limit distributions and variance bounds for particle current in several dynamical stochastic systems of particles on the one-dimensional integer lattice: independent particles, independent particles in a random environment, the random average process, the asymmetric simple exclusion process, and a class of totally asymmetric… (More)

- Júlia Komjáthy, D. M. Kunick
- 2003

- Shankar Bhamidi, Remco van der Hofstad, Júlia Komjáthy
- J. Applied Probability
- 2014

In this paper we establish a connection between epidemic models on random networks with general infection times considered in [2] and first passage percolation. Using techniques developed in [6], when each vertex has infinite contagious periods, we extend results on the epidemic curve in [2] from bounded degree graphs to general sparse random graphs with… (More)

• A submitted manuscript is the author's version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the… (More)

- Enrico Baroni, Remco van der Hofstad, Júlia Komjáthy
- J. Applied Probability
- 2017

These notes discuss limit distributions and variance bounds for particle current in several systems of particles on the one-dimensional integer lattice: independent random walks, independent random walks in a random environment, the random average process, the asymmetric simple exclusion process, and a class of zero range processes. The text is based on… (More)