Search results for "Large numbers"

Cluster Analysis Tailored to Structure Change of Tropical Cyclones Using a Very Large Number of Trajectories

2020

AbstractMajor airstreams in tropical cyclones (TCs) are rarely described from a Lagrangian perspective. Such a perspective, however, is required to account for asymmetries and time dependence of the TC circulation. We present a procedure that identifies main airstreams in TCs based on trajectory clustering. The procedure takes into account the TC’s large degree of inherent symmetry and is suitable for a very large number of trajectories . A large number of trajectories may be needed to resolve both the TC’s inner-core convection as well as the larger-scale environment. We define similarity of trajectories based on their shape in a storm-relative reference frame, rather than on proximity in …

A True Extension of the Markov Inequality to Negative Random Variables

2020

The Markov inequality is a classical nice result in statistics that serves to demonstrate other important results as the Chebyshev inequality and the weak law of large numbers, and that has useful applications in the real world, when the random variable is unspecified, to know an upper bound for the probability that an variable differs from its expectation. However, the Markov inequality has one main flaw: its validity is limited to nonnegative random variables. In the very short note, we propose an extension of the Markov inequality to any non specified random variable. This result is completely new.

Scaling properties of topologically random channel networks

1996

Abstract The analysis deals with the scaling properties of infinite topologically random channel networks (ITRNs) fast introduced by Shreve (1967, J. Geol. , 75: 179–186) to model the branching structure of rivers as a random process. The expected configuration of ITRNs displays scaling behaviour only asymptotically, when the ruler (or ‘yardstick’) length is reduced to a very small extent. The random model can also reproduce scaling behaviour at larger ruler lengths if network magnitude and diameter are functionally related according to a reported deterministic rule. This indicates that subsets of rrRNs can be scaling and, although rrRNs are asymptotically plane-filling due to the law of la…

Law of the Iterated Logarithm

2020

For sums of independent random variables we already know two limit theorems: the law of large numbers and the central limit theorem. The law of large numbers describes for large \(n\in \mathbb{N}\) the typical behavior, or average value behavior, of sums of n random variables. On the other hand, the central limit theorem quantifies the typical fluctuations about this average value.

On the Talmud Division: Equity and Robustness

2008

The Talmud Division is a very old method of sharin g developed by the rabbis in the Talmud and brought to the fore in the modern area s ome authors, among them are Aumann and Maschler. One compares the Talmud Division to other methods, mainly here the most popular, Aristotle's Proportional Division, but also to the equal division. The Talmud Division is more egalitarian than the Proportional Division for smal l levels of estate and conversely and it protects the weakest -those who cannot place a non-zero clai m-. This suggests that claimants may choose among the claiming methods depending on their interest, what implies a metagame. Unlike other methods as the Proportional Division, the Talm…

The “Gentle Law” of Large Numbers: Stifter’s Urban Meteorology

2020

Moments and Laws of Large Numbers

2020

The most important characteristic quantities of random variables are the median, expectation and variance. For large n, the expectation describes the typical approximate value of the arithmetic mean (X 1+…+X n )/n of independent and identically distributed random variables (law of large numbers).

A SIMPLE PARTICLE MODEL FOR A SYSTEM OF COUPLED EQUATIONS WITH ABSORBING COLLISION TERM

2011

We study a particle model for a simple system of partial differential equations describing, in dimension $d\geq 2$, a two component mixture where light particles move in a medium of absorbing, fixed obstacles; the system consists in a transport and a reaction equation coupled through pure absorption collision terms. We consider a particle system where the obstacles, of radius $\var$, become inactive at a rate related to the number of light particles travelling in their range of influence at a given time and the light particles are instantaneously absorbed at the first time they meet the physical boundary of an obstacle; elements belonging to the same species do not interact among themselves…

The Vlasov Limit for a System of Particles which Interact with a Wave Field

2008

In two recent publications [Commun. PDE, vol.22, p.307--335 (1997), Commun. Math. Phys., vol.203, p.1--19 (1999)], A. Komech, M. Kunze and H. Spohn studied the joint dynamics of a classical point particle and a wave type generalization of the Newtonian gravity potential, coupled in a regularized way. In the present paper the many-body dynamics of this model is studied. The Vlasov continuum limit is obtained in form equivalent to a weak law of large numbers. We also establish a central limit theorem for the fluctuations around this limit.

Vanishing chiral couplings in the large-Nc resonance theory

2007

5 pages, 2 figures.-- PACS nrs.: 12.39.Fe; 11.15.Pg; 12.38.-t.-- ISI Article Identifier: 000247625300022.-- ArXiv pre-print available at: http://arxiv.org/abs/hep-ph/0611375