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Growth of Random Surfaces

Borodin, Alexei (2011) Growth of Random Surfaces. In: Proceedings of the International Congress of Mathematicians 2010 (ICM 2010). Hindustan Book Agency , New Delhi, pp. 2188-2202. ISBN 978-981-4324-30-4.

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We describe a class of exactly solvable random growth models of one and two-dimensional interfaces. The growth is local (distant parts of the interface grow independently), it has a smoothing mechanism (fractal boundaries do not appear), and the speed of growth depends on the local slope of the interface. The models enjoy a rich algebraic structure that is reflected through closed determinantal formulas for the correlation functions. Large time asymptotic analysis of such formulas reveals asymptotic features of the emerging interface in different scales. Macroscopically, a deterministic limit shape phenomenon can be observed. Fluctuations around the limit shape range from universal laws of Random Matrix Theory to conformally invariant Gaussian processes in the plane. On the microscopic (lattice) scale, certain universal determinantal random point processes arise.

Item Type:Book Section
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Additional Information:© 2011 World Scientific Publishing Co Pte Ltd.
Subject Keywords:Random growth; determinantal point processes; Gaussian free field
Classification Code:AMSC: Primary 82C41, Secondary 60B10, Secondary 60G55, Secondary 60K35
Record Number:CaltechAUTHORS:20180807-142408625
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Official Citation:Growth of Random Surfaces. Alexei Borodin Proceedings of the International Congress of Mathematicians 2010 (ICM 2010). June 2011, 2188-2202
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:88635
Deposited By: Tony Diaz
Deposited On:07 Aug 2018 21:33
Last Modified:03 Oct 2019 20:08

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