The perimeter of uniform and geometric words: a probabilistic analysis

Let a word be a sequence of $n$ i.i.d. integer random variables. The perimeter $P$ of the word is the number of edges of the word, seen as a polyomino. In this paper, we present a probabilistic approach to the computation of the moments of $P$. This is applied to uniform and geometric random variables. We also show that, asymptotically, the distribution of $P$ is Gaussian and, seen as a stochastic process, the perimeter converges in distribution to a Brownian motionComment: 13 pages, 7 figure

The perimeter of uniform and geometric words: a probabilistic analysis

Let a word be a sequence of $n$ i.i.d. integer random variables. The perimeter $P$ of the word is the number of edges of the word, seen as a polyomino. In this paper, we present a probabilistic approach to the computation of the moments of $P$. This is applied to uniform and geometric random variables. We also show that, asymptotically, the distribution of $P$ is Gaussian and, seen as a stochastic process, the perimeter converges in distribution to a Brownian motionComment: 13 pages, 7 figure

Hard Cases Under the Convention on the International Sale of Goods: A Proposed Taxonomy of Interpretative Challenges

CISG was formally uniform at the time of its adoption. It used the same words in all of the jurisdictions adopting it. But uniform words are not enough to guarantee uniform application. For many commentators, in fact, the most significant impediment to the continued existence or efficacy of the CISG is the lack of uniform interpretive outcomes in hard CISG cases – cases where a CISG provision is vague either on its face or in its application. Without greater uniformity of interpretive outcomes, these commentators suggest, the CISG will, over time, fail to supply standard solutions to similar contracting problems and thus fail to supply the predictability that parties need. In this Article, Professor Allen Blair argues that these commentators start with an exaggerated expectation about the kind and degree of uniformity called for by the CISG and demanded by parties. Contrary to the standard conception of CISG interpretation, uniformity of interpretive outcomes is an improper goal with respect to CISG provisions cast as open-textured standards, and any effort to harden these standards into rigid rules could, in fact, undermine the efficiency goals of contracting parties

Uniform Random Sampling of Traces in Very Large Models

This paper presents some first results on how to perform uniform random walks (where every trace has the same probability to occur) in very large models. The models considered here are described in a succinct way as a set of communicating reactive modules. The method relies upon techniques for counting and drawing uniformly at random words in regular languages. Each module is considered as an automaton defining such a language. It is shown how it is possible to combine local uniform drawings of traces, and to obtain some global uniform random sampling, without construction of the global model