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A Limit Law for the Root Value of Minimax Trees
Minimax Tree Limit Law Weak Convergence Analysis of Algorithms Gametree
2009/4/27
We consider minimax trees with independent, identically distributed leaf values that have a continuous distribution function FV being strictly increasing on the range where 0< FV <1. It was shown by P...
Strong Law of Large Numbers Under a General Moment Condition
quasi-stationary sequence strong law of large numbers maximum inequality
2009/4/27
We use our maximum inequality for p-th order random variables (p>1) to prove a strong law of large numbers (SLLN) for sequences of p-th order random variables. In particular, in the case p=2 our resu...
On the Zero-One Law and the Law of Large Numbers for Random Walk in Mixing Random Environment
Random walk random environment zero-one law law of large numbers
2009/4/24
We prove a weak version of the law of large numbers for multi-dimensional finite range random walks in certain mixing elliptic random environments. This already improves previously existing results, w...
Book Review:Making Labour Law in Australia: Industrial Relations, Politics and Law
Book Review Labour Law Australia Industrial Relations Politics Law
2009/4/21
In Making Labour Law in Australia, Laura Bennett (1994) disputes orthodox legal scholarship’s conviction that received Australian labour law is immutable. Bennett considers that courts, tribunals, emp...
On the Zero-One Law and the Law of Large Numbers for Random Walk in Mixing Random Environment
Zero-One Law Random Walk Mixing Random Environment
2009/4/7
We prove a weak version of the law of large numbers for multi-dimensional finite range random walks in certain mixing elliptic random environments. This already improves previously existing results, w...
Convergence，Strong Law of Large Numbers，and Measurement Theory in the Language of Fuzzy Variables
Convergence Strong Law Large Numbers Measurement Theory Fuzzy Variables
2010/3/19
In the paper we define the convergence of compact fuzzy sets as a convergence of -cuts in
the topology of compact subsets of a metric space. Furthermore we define typical convergences of
fuzzy vari...
On the strong law of large numbers for d-dimensional arrays of random variables
large numbers d-dimensional arrays random variables
2009/3/31
In this paper, we provide a necessary and sufficient condition for general d-dimensional arrays of random variables to satisfy strong law of large numbers. Then, we apply the result to obtain some str...
The zero-one law for planar random walks in i.i.d. random environments revisited
zero-one law random walk ergodic property
2009/3/30
In this note we present a simplified proof of the zero-one law by Merkl and Zerner (2001) for directional transience of random walks in i.i.d. random environments (RWRE) on the square lattice. Also, w...
A probabilistic proof of a weak limit law for the number of cuts needed to isolate the root of a random recursive tree
weak limit law random recursive tree random walk
2009/3/23
We present a short probabilistic proof of a weak convergence result for the number of cuts needed to isolate the root of a random recursive tree. The proof is based on a coupling related to a certain ...
Explicit Bounds for the Approximation Error in Benford's Law
Approximation Error Benford's Law
2009/3/19
Benford’s law states that for many random variables X > 0 its leading digit D = D(X) satisfies approximately the equation ℙ(D = d) = log 10(1 + 1∕d) for d = 1,2,…,9. This phenomenon follows from...
Power-law distributions in empirical data
Power-law distributions Pareto Zipf maximum likelihood heavy-tailed distributions likelihood ratio test model selection
2010/4/29
Power-law distributions occur in many situations of scientific interest and have
significant consequences for our understanding of natural and man-made phenomena. Unfortunately,the detection and char...
A Law of Likelihood for Composite Hypotheses
likelihood paradigm likelihood ratio profile likelihood statistical evidence support interval support set
2010/3/17
The law of likelihood underlies a general framework, known as the likelihood paradigm, for representing
and interpreting statistical evidence. As stated, the law applies only to simple hypotheses, an...
PARKS, PROPERTY RIGHTS, AND THE POSSIBILITIES OF THE PRIVATE LAW
private property rights PRIVATE LAW national parks governmental ownership
2008/12/24
It is commonly assumed that private property rights are incompatible
with the preservation of such environmental and recreational
amenities as our national parks and that governmental ownership
is ...
What do law libraries and the Great Wall of China have in common? They combined for a great trip that included professional and cultural learning for a group of Special Libraries Association (SLA) mem...
Introduction: Law as a Normative Discipline
Law is a set of commands; the principles of tort or criminal law,
which we shall be dealing with, are negative commands or prohibitions,
on the order of ...