We derive an explicit representation for p-adic Feynman and Koba-Nielsen amplitudes and we briefly outline the connection between the scalar models of p»adic quantum field theory and Dyson's hierarchical models.
We model the generation of words with independent unequal probabilities of occurrence of letters. We prove that the probability p(r) of occurrence of words of rank r has a power asymptotics. As distinct from the paper published earlier by B. Conrad and M. Mitzenmacher, we give a brief proof by elementary methods and obtain an explicit formula for the exponent of the power law.
Consider a homogeneous Markov chain with discrete time and with a finite set of states E 0 ,. .. , En such that the state E 0 is absorbing and states E 1 ,. .. , En are nonrecurrent. The frequencies of trajectories in this chain are studied in this paper, i.e., "words" composed of symbols E 1 ,. .. , En ending with the "space" E 0. Order the words according to their probabilities; denote by p(t) the probability of the t th word in this list. As was proved recently, in the case of an infinite list of words, in the dependence of the topology of the graph of the Markov chain, there exists either the limit ln p(t)/ ln t as t → ∞ or that of ln p(t)/t 1/D , where D ∈ N (weak power and subexponential laws). As appeared, in the latter case the decreasing order of the function p(t) is always subexponential (the strong subexponential law). In the first case, this paper describes necessary and sufficient conditions of the power order (the strong power law). These conditions are fulfilled, in particular, if the graph of the Markov chain that corresponds to states E 1 ,. .. , En is strongly connected.
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.