"Typically, models with a heterogeneous property are considerably harder to analyze than the corresponding homogeneous models, in which the heterogeneous property is replaced with its average value. In this study we show that any outcome of a heterogeneous model that satisfies the two properties of emph{differentiability} and emph{interchangibility}, is $O(epsilon^2)$ equivalent to the outcome of the corresponding homogeneous model, where $epsilon$ is the level of heterogeneity. We then use this emph{averaging principle} to obtain new results in queueing theory, game theory (auctions), and social networks (marketing)."

--- The claim in the abstract seems far too general to be true.

"The theory of large deviations has been applied successfully in the last 30 years or so to study the properties of equilibrium systems and to put the foundations of equilibrium statistical mechanics on a clearer and more rigorous footing. A similar approach has been followed more recently for nonequilibrium systems, especially in the context of interacting particle systems. We review here the basis of this approach, emphasizing the similarities and differences that exist between the application of large deviation theory for studying equilibrium systems on the one hand and nonequilibrium systems on the other. Of particular importance are the notions of macroscopic, hydrodynamic, and long-time limits, which are analogues of the equilibrium thermodynamic limit, and the notion of statistical ensembles which can be generalized to nonequilibrium systems. For the purpose of illustrating our discussion, we focus on applications to Markov processes, in particular to simple random walks."

"A discrete agent-based model on a periodic lattice of arbitrary dimension is considered. Agents move to nearest-neighbor sites by a motility mechanism accounting for general interactions, which may include volume exclusion. The partial differential equation describing the average occupancy of the agent population is derived systematically. A diffusion equation arises for all types of interactions and is nonlinear except for the simplest interactions. In addition, multiple species of interacting subpopulations give rise to an advection-diffusion equation for each subpopulation. This work extends and generalizes previous specific results, providing a construction method for determining the transport coefficients in terms of a single conditional transition probability, which depends on the occupancy of sites in an influence region. These coefficients characterize the diffusion of agents in a crowded environment in biological and physical processes."

We construct and analyze a climate network which represents the interdependent structure of the climate in different geographical zones and find that the network responds in a unique way to El Niño events. Analyzing the dynamics of the climate network shows that when El Niño events begin, the El Niño basin partially loses its influence on its surroundings. After typically three months, this influence is restored while the basin loses almost all dependence on its surroundings and becomes autonomous. The formation of an autonomous basin is the missing link to understand the seemingly contradicting phenomena of the afore-noticed weakening of the interdependencies in the climate network during El Niño and the known impact of the anomalies inside the El Niño basin on the global climate system.

"A new stochastic mode-elimination procedure is introduced for a class of deterministic systems. Under assumptions of ergodicity and mixing, the procedure gives closed-form stochastic models for the slow variables in the limit of infinite separation of timescales. The procedure is applied to the truncated Burgers–Hopf (TBH) system as a test case where the separation of timescale is only approximate. It is shown that the stochastic models reproduce exactly the statistical behaviour of the slow modes in TBH when the fast modes are artificially accelerated to enforce the separation of timescales. It is shown that this operation of acceleration only has a moderate impact on the bulk statistical properties of the slow modes in TBH. As a result, the stochastic models are sound for the original TBH system."

"... we have good models for material behaviors at small and large scales ...  hard to relate these ... models to one another. Macroscale models represent the integrated effects of very subtle factors that are practically invisible at the smallest, atomic, scales. ... notoriously difficult to model realistic materials with a simple bottom-up-from-the-atoms strategy.... forced physicists interested in overall macro-behavior of materials toward completely top-down modeling strategies familiar from traditional continuum mechanics. ...  whether we can exploit our rather rich knowledge of intermediate micro- (or meso-) scale behaviors in a manner that would allow us to bridge between these two dominant methodologies. Macroscopic scale behaviors often fall into large common classes of behaviors such as the class of isotropic elastic solids, characterized by two ... elastic coefficients. Can we employ knowledge of lower scale behaviors to ... determine the coefficients ... ?"

"From my perspective, the strange thing is that people kept trying to prove uniqueness and stability of general equilibrium.
Simply look at: [time-series of US employment to population ratio] and try to avoid the conclusion that to first order the U.S. economy can be in at least meta-stable equilibrium with an adult employment-to-population ratio of about 63% or with an adult employment-to-population ratio of 58.5%--and probably anywhere in between as well.
Proposing that economists pursue the research program of demonstrating that the economy has a unique stable equilibrium has thus always seemed to me to be like proposing that physicists pursue the research program of demonstrating the feathers fall unusually rapidly..."

In a public form, at last.

Looks interesting, and co-edited by my old office mate Troy.  (Oh, and Blake has a paper as well!)  ETA: We don't subscribe. :(

Giving thanks for the applicability of effective field theory. Part of me wants to say "You mis-spelled 'laws of large numbers', HTH, HAND.", but in the sprit of the occasion I will forbear.

"We present recent results on coarse-graining techniques for thermodynamic quantities (canonical averages) and dynamical quantities (averages of path functionals over solutions of overdamped Langevin equations). The question is how to obtain reduced models to compute such quantities, in the specific case when the functional to be averaged only depends on a few degrees of freedom. We mainly review, numerically illustrate and extend results from [3,18], concerning the computation of the stress-strain relation for one-dimensional chains of atoms, and the construction of an effective dynamics for a scalar coarse-grained variable when the complete system evolves according to the overdamped Langevin equation." --- The abstract reminds me of Eyink's optimal-approximting-equations approach, based on large deviations theory.

"A hitherto neglected form of explanation is explored, especially its role in population genetics. “Statistically abstractive explanation” (SA explanation) mandates the suppression of factors probabilistically relevant to an explanandum when these factors are extraneous to the theoretical project being pursued. When these factors are suppressed, the explanandum is rendered uncertain. But this uncertainty traces to the theoretically constrained character of SA explanation, not to any real indeterminacy. Random genetic drift is an artifact of such uncertainty, and it is therefore wrong to reify it as a cause of evolution or as a process in its own right."

Sounds promising, but much depends on the model, about which he is vague here.

My reaction to the first half is "preach it, brothers and sisters!" Perhaps inevitably, the constructive proposals of the 2nd half are less compelling.

"This book provides the first rigorous derivation of mesoscopic and macroscopic equations from a deterministic system of microscopic equations. The microscopic equations are cast in the form of a deterministic (Newtonian) system of coupled nonlinear oscillators for N large particles and infinitely many small particles. The mesoscopic equations are stochastic ordinary differential equations (SODEs) and stochastic partial differential equatuions (SPDEs), and the macroscopic limit is described by a parabolic partial differential equation."

Or: "The fixity of the internal environment is the condition for free life."

Sounds _very much_ like the old Fox & Keizer papers (PRL 64 [1990]: 249 and PRA 43 [1991]: 1709) on "amplification of intrinsic molecular fluctuations by chaos"; but those aren't cited. Read carefully; write a comment?

Damn you, Clark! (Not really.)

One of the creators surveys the field. Wald Lecture for 2005.