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We present general results for the contact process by a method which applies to all transitive graphs of bounded degree, including graphs of exponential growth. The model's infection rates are varied through a control parameter, for which two natural transition points are defined as: i. λT , the value up to which the infection dies out exponentially fast if(More)
The invariant measures I for the exclusion process have long been studied and a complete description is known in many cases. This paper gives characterizations of I for exclusion processes on Z with certain reversible transition kernels. Some examples for which I is given include all finite range kernels that are asymptotically equal to p(x, x + 1) = p(x, x(More)
Environmental health science is the study of the impact of the environment on human health. This paper introduces basic topics in environmental health, including clean air, clean water, and healthful food, as well as a range of current issues and controversies in environmental health. Conceptual shifts in modern toxicology have changed the field. There is a(More)
The symmetric exclusion process and the voter model are two interacting particle systems for which a dual finite particle system allows one to characterize its invariant measures. Adding spontaneous births and deaths to the two processes still allows one to use the dual process to obtain information concerning the original process. This paper introduces the(More)
Using the framework of random walks in random scenery, Cohen and Samorodnitsky (2006) introduced a family of symmetric α-stable motions called local time fractional stable motions. When α = 2, these processes are precisely fractional Brownian motions with 1/2 < H < 1. Motivated by random walks in alternating scenery, we find a complementary family of(More)
We present general results for the contact process by a method which applies to all transitive graphs of bounded degree, including graphs of exponential growth. The model's infection rates are varied though a common control parameter, for which two natural transition points are defined as: i. λT , the value up to which the infection dies out exponentially(More)
Page 5, lines 1-4↑. The q-matrix referred to here follows the usual convention: It is chosen to have negative diagonal entries so that the row sums are zero. Page 39, line 9↑. " were " should be " where ". Page 46, line 15↓. " mininmum " should be " minimum ". Also, add: " Jensen's inequality implies that " Pages 48-54. Several readers have pointed out that(More)