We provide an explicit construction of the thermodynamic jamming limit for the parking process and other finite range exclusion schemes on Z d . By means thereof, a strong law of large numbers for occupation densities is accomplished, and, amongst other results, the so called "super-exponential" (i.e. gamma) decay of pair correlation functions is established.2 In a sense to be specified in subsection 5.2. 3 a measure space whose σ-algebra is generated by a topology which is metrizable, complete
We present a coupled decreasing sequence of random walks on Z (X (i) . , i ∈ N) that dominates the edge process of oriented-bond percolation in two dimensions. Using the concept of "random walk in a strip ",we construct an algorithm that generates an increasing sequence of lower bounds that converges to the critical probability of oriented-bond percolation. Numerical calculations of the first ten lower bounds thereby generated lead to an improved,ie higher, rigorous lower bound to this critical probability, viz. pc ≥ 0.63328. Finally a computer simulation technique is presented; the use thereof establishes 0.64450 as a non-rigorous five-digit-precision (lower) estimate for pc.
Oliveira -IF-USP • Prof ª. Dra. Nancy Garcia Lopes -IMECC-UNICAMP lJl Agradecimentos Ao CNPQ pelo apoio financeiro e ao Professor Mikhail h/lenshikov por sua contribuição à formulação deste trabalho.
AgradecimentosAo CNPQ pelo apoio financeiro e ao Professor Mikhail Menshikov por sua contribuição à formulação deste trabalho.
V
ResumoApresentamos uma sequência decrescente de passeios aleatórios em Z , que domina a margem díreiZa do processo de percolação orientada. Através do conceito de cadeia de .l/arcou numa /alfa, descrevemos um algoritmo que gera uma seqüência crescente de quotas inferiores que converge para a probabilidade crítica do processo de percolação orientada em duas dimenssões. Calculando numericamente os dez primeiros termos dessa seqüência, obtivemos uma nova quota inferior para a probabilidade crítica deste processo:
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.