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Continuum Limits for Classical Sequential Growth Models by Graham Brightwell; Nicholas Georgiou is a Mathematics article available to read on EtoBox.

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## Abstract A random graph order, also known as a transitive percolation process, is defined by taking a random graph on the vertex set {0,...,__n__ − 1} and putting __i__ below __j__ if there is a path __i__ = __i__~1~...__i__~__k__~ = __j__ in the graph with __i__~1~ < ... < __i__~__k__~. Rideout and Sorkin Phys. Rev. D 63 (2001) 104011 provide computational evidence that suitably normalized sequences of random graph orders have a “continuum limit.” We confirm that this is the case and show that the continuum limit is always a semiorder. Transitive percolation processes are a special case of a more general class called classical sequential growth models. We give a number of results describing the large‐scale structure of a general classical sequential growth model. We show that for any sufficiently large __n__, and any classical sequential growth model, there is a semiorder __S__ on {0,...,__n__ ‐ 1} such that the random partial order on {0,...,__n__ ‐ 1} generated according to the model differs from __S__ on an arbitrarily small proportion of pairs. We also show that, if any sequence of classical sequential growth models has a continuum limit, then this limit is (essentially) a

Who reads Continuum Limits for Classical Sequential Growth Models?

Author

Graham Brightwell; Nicholas Georgiou

Publisher

John Wiley and Sons; Wiley (John Wiley & Sons); John Wiley & Sons Inc.; Wiley (ISSN 1042-9832)

Published

2009

Language

EN

Field

Mathematics (Physical Sciences)