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In and Out of Equilibrium 2

Part of the Progress in Probability Book Series (volume 60)

Editors: Sidoravicius, Vladas; Vares, Maria Eulália

DOI: 10.1007/978-3-7643-8786-0

ISBN: 978-3-7643-8785-3

Publisher: Birkhäuser Basel - Springer Journals

Jan 1, 2008

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Chapter 21Gibbsian Description of Mean-Field Models

Le Ny, Arnaud

Pages: 463 –480

[We introduce a new framework to describe mean-field models in the spirit of the DLR description of probability measures on infinite prodnet probability spaces used for lattice spin systems. The approach, originally introduced by C. Kuelske in 2003, is inspired by the generalized Gibbsian...
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Chapter 22What is the Difference Between a Square and a Triangle?

Limic, Vlada; Tarrès, Pierre

Pages: 481 –495

[We offer a reader-friendly introduction to the attracting edge problem (also known as the “triangle conjecture”) and its most general current solution of Limic and Tarrès (2007). Little original research is reported; rather this article “zooms in” to describe the essential characteristics of two...
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Chapter 23Long-Range Dependence in Mean and Volatility: Models, Estimation and Forecasting

Lopes, Sílvia R. C.

Pages: 497 –525

[In this paper we consider the estimation and forecasting future values of some stochastic processes exhibiting long-range dependence, both in mean and in volatility. We summarize basic definitions, properties and some results considering ARFIMA and SARFIMA processes, which exhibit long memory in...
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Chapter 24Percolation in the Sherrington-Kirkpatrick Spin Glass

Machta, J.; Newman, C. M.; Stein, D. L.

Pages: 527 –542

[We present extended versions and give detailed proofs of results about percolation (using various sets of two-replica bond occupation variables) in Sherrington-Kirkpatrick spin glasses (with zero external field) that were first given in an earlier paper by the same authors. We also explain how...
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Chapter 25A Note on the Diffusivity of Finite-Range Asymmetric Exclusion Processes on ℤ

Quastel, Jeremy; Valkó, Benedek

Pages: 543 –549

[The diffusivity D(t) of finite-range asymmetric exclusion processes on ℤ with non-zero drift is expected to be of order t1/3. Seppäläinen and Balázs recently proved this conjecture for the nearest neighbor case. We extend their results to general finite range exclusion by proving that the...
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Chapter 26On the Role of Spatial Aggregation in the Extinction of a Species

Schinazi, Rinaldo B.

Pages: 551 –557

[We compare two spatial stochastic models. The first, introduced by Schinazi (2005), shows that spatial aggregation may cause the extinction of a species in catastrophic times. The second shows that, for a certain range of parameters, spatial aggregation may help the survival of a species in non...
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Chapter 27Systems of Random Equations. A Review of Some Recent Results

Wschebor, Mario

Pages: 559 –574

[We review recent results on moments of the number of real roots of random systems of equations. The emphasis is on large polynomial systems, although the last section is on non-polynomial ones. We give no proofs, excepting for a short proof of the now classical Shub-Smale Theorem (1993) which...

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