The Dale Oil Field, Caldwell County, Texas

Geological Science

Stationary distributions of the multi-type ASEP

We give a recursive construction of the stationary distribution of multi-type asymmetric simple exclusion processes on a finite ring or on the infinite line $Z$. The construction can be interpreted in terms of "multi-line diagrams" or systems of queues in tandem. Let $q$ be the asymmetry parameter of the system. The queueing construction generalises the one previously known for the totally asymmetric ($q=0$) case, by introducing queues in which each potential service is unused with probability $q^k$ when the queue-length is $k$. The analysis is based on the matrix product representation of Prolhac, Evans and Mallick. Consequences of the construction include: a simple method for sampling exactly from the stationary distribution for the system on a ring; results on common denominators of the stationary probabilities, expressed as rational functions of $q$ with non-negative integer coefficients; and probabilistic descriptions of "convoy formation" phenomena in large systems.Comment: 54 pages, 4 figure

Reconstruction thresholds on regular trees

We consider a branching random walk with binary state space and index set $T^k$, the infinite rooted tree in which each node has k children (also known as the model of "broadcasting on a tree"). The root of the tree takes a random value 0 or 1, and then each node passes a value independently to each of its children according to a 2x2 transition matrix P. We say that "reconstruction is possible" if the values at the d'th level of the tree contain non-vanishing information about the value at the root as $d\to\infty$. Adapting a method of Brightwell and Winkler, we obtain new conditions under which reconstruction is impossible, both in the general case and in the special case $p_{11}=0$. The latter case is closely related to the "hard-core model" from statistical physics; a corollary of our results is that, for the hard-core model on the (k+1)-regular tree with activity $\lambda=1$, the unique simple invariant Gibbs measure is extremal in the set of Gibbs measures, for any k.Comment: 12 page

LAND-GRANT ORGANIZATION TO MEET THE FUTURE

Teaching/Communication/Extension/Profession,

Terrorism and the resilience of cities

The September 11 attacks in New York and Washington have forced Americans to confront the fact that to live or work in a large city is to be at greater risk of large-scale terrorism. What do these risks, and the public perception of them, imply for cities in general and the future of New York City in particular? In this article, the authors begin their exploration of this issue by examining why cities exist in the first place. To conduct their analysis, they simulate two key theoretical models of economic geography, using data that approximate the characteristics of a major U.S. city as well as estimates of the costs of the September 11 attacks. The authors conclude that the very forces that lead to city formation also lead cities to be highly resilient in the face of catastrophes such as terrorist attacks. They argue that New York City in particular is likely to continue to thrive despite any ongoing terrorist threat.War - Economic aspects ; Urban economics ; Cities and towns ; Economic conditions - New York (N.Y.) ; Federal Reserve District, 2nd

An economic analysis of liquidity-saving mechanisms

A recent innovation in large-value payments systems has been the design and implementation of liquidity-saving mechanisms (LSMs), tools used in conjunction with real-time gross settlement (RTGS) systems. LSMs give system participants, such as banks, an option not offered by RTGS alone: they can queue their outgoing payments. Queued payments are released if some prespecified event occurs. LSMs can reduce the amount of central bank balances necessary to operate a payments system as well as quicken settlement. This article analyzes the performance of RTGS systems with and without the addition of an LSM. The authors find that, in terms of settling payments early, these mechanisms typically outperform pure RTGS systems. However, there are times when RTGS systems can be preferable to LSMs, such as when many banks that send payments early in RTGS choose to queue their payments when an LSM is available. The authors also show that the design of a liquidity-saving mechanism has important implications for the welfare of system participants, even in the absence of payment netting. In particular, the parameters specified determine whether the addition of an LSM increases or decreases welfare.Payment systems ; Banks and banking, Central ; Bank liquidity

How to squeeze the toothpaste back into the tube

We consider "bridges" for the simple exclusion process on Z, either symmetric or asymmetric, in which particles jump to the right at rate p and to the left at rate 1-p. The initial state O has all negative sites occupied and all non-negative sites empty. We study the probability that the process is again in state O at time t, and the behaviour of the process on [0,t] conditioned on being in state O at time t. In the case p=1/2, we find that such a bridge typically goes a distance of order t (in the sense of graph distance) from the initial state. For the asymmetric systems, we note an interesting duality which shows that bridges with parameters p and 1-p have the same distribution; the maximal distance of the process from the original state behaves like c(p)log(t) for some constant c(p) depending on p. (For p>1/2, the front particle therefore travels much less far than the bridge of the corresponding random walk, even though in the unconditioned process the path of the front particle dominates a random walk.) We mention various further questions.Comment: 15 page