Public Goals, Property Values, and Regional Cooperation

Do public officials care about property values? If so, are their decisions about tax rates, public spending, land use, and regional cooperation paying off? Fiscal and land use data for Connecticut’s 169 towns offer some insights about development patterns and how local public policies may affect the value of real property—structures and land. We look at the effects of municipal tax, spending and land-use policies, as well as the impact of regional cooperation—in the form of regional school districts—on the value of real property per acre of available land. Fiscal policies and the level of development have the anticipated effects on property values, but the impact of participation in regional high school districts is less clear.

Comment on "Towards a large deviation theory for strongly correlated systems"

I comment on a recent paper by Ruiz and Tsallis [Phys. Lett. A 376, 2451 (2012)] claiming to have found a '$q$-exponential' generalization of the large deviation principle for strongly correlated random variables. I show that the basic scaling results that they find numerically can be reproduced with a simple example involving independent random variables, and are not specifically related to the $q$-exponential function. In fact, identical scaling results can be obtained with any other power-law deformations of the exponential. Thus their results do not conclusively support their claim of a $q$-exponential generalization of the large deviation principle.Comment: Comment, 3 pages, 2 figure

Bouchaud-M\'ezard model on a random network

We studied the Bouchaud-M\'ezard(BM) model, which was introduced to explain Pareto's law in a real economy, on a random network. Using "adiabatic and independent" assumptions, we analytically obtained the stationary probability distribution function of wealth. The results shows that wealth-condensation, indicated by the divergence of the variance of wealth, occurs at a larger $J$ than that obtained by the mean-field theory, where $J$ represents the strength of interaction between agents. We compared our results with numerical simulation results and found that they were in good agreement.Comment: to be published in Physical Review

On the Extreme Flights of One-Sided Levy Processes

We explore the statistical behavior of the order statistics of the flights of One-sided Levy Processes (OLPs). We begin with the study of the extreme flights of general OLPs,and then focus on the class of selfsimilar processes,investigating the following issues:(i)the inner hierarchy of the extreme flights - for example:how big is the 7th largest flight relative to the 2nd largest one?; and,(ii)the relative contribution of the extreme flights to the entire 'flight aggregate' - for example: how big is the 3rd largest flight relative to the OLP's value?. Furthermore, we show that all 'hierarchical' results obtained - but not the 'aggregate' results - are explicitly extendable to the class of OLPs with arbitrary power-law flight tails (which is far larger than the selfsimilar class).Comment: 21 pages. This manuscript is an extended version of a contribution to a special Physica A volume in honor of Shlomo Havlin on his sixtieth birthda

Edgeworth expansions in operator form

An operator form of asymptotic expansions for Markov chains is established. Coefficients are given explicitly. Such expansions require a certain modification of the classical spectral method. They prove to be extremely useful within the context of large deviations.Comment: 12 page

Thermodynamics of the L\'evy spin glass

We investigate the L\'evy glass, a mean-field spin glass model with power-law distributed couplings characterized by a divergent second moment. By combining extensively many small couplings with a spare random backbone of strong bonds the model is intermediate between the Sherrington-Kirkpatrick and the Viana-Bray model. A truncated version where couplings smaller than some threshold \eps are neglected can be studied within the cavity method developed for spin glasses on locally tree-like random graphs. By performing the limit \eps\to 0 in a well-defined way we calculate the thermodynamic functions within replica symmetry and determine the de Almeida-Thouless line in the presence of an external magnetic field. Contrary to previous findings we show that there is no replica-symmetric spin glass phase. Moreover we determine the leading corrections to the ground-state energy within one-step replica symmetry breaking. The effects due to the breaking of replica symmetry appear to be small in accordance with the intuitive picture that a few strong bonds per spin reduce the degree of frustration in the system

Simple observations concerning black holes and probability

It is argued that black holes and the limit distributions of probability theory share several properties when their entropy and information content are compared. In particular the no-hair theorem, the entropy maximization and holographic bound, and the quantization of entropy of black holes have their respective analogues for stable limit distributions. This observation suggests that the central limit theorem can play a fundamental role in black hole statistical mechanics and in a possibly emergent nature of gravity.Comment: 6 pages Latex, final version. Essay awarded "Honorable Mention" in the Gravity Research Foundation 2009 Essay Competitio

Hidden Variables in Bipartite Networks

We introduce and study random bipartite networks with hidden variables. Nodes in these networks are characterized by hidden variables which control the appearance of links between node pairs. We derive analytic expressions for the degree distribution, degree correlations, the distribution of the number of common neighbors, and the bipartite clustering coefficient in these networks. We also establish the relationship between degrees of nodes in original bipartite networks and in their unipartite projections. We further demonstrate how hidden variable formalism can be applied to analyze topological properties of networks in certain bipartite network models, and verify our analytical results in numerical simulations