Record statistics for a discrete-time random walk with correlated steps
نویسندگان
چکیده
منابع مشابه
Random walk with shrinking steps
We outline the properties of a symmetric random walk in one dimension in which the length of the nth step equals l, with l,1. As the number of steps N→` , the probability that the end point is at x approaches a limiting distribution Pl(x) that has many beautiful features. For l,1/2, the support of Pl(x) is a Cantor set. For 1/2<l,1, there is a countably infinite set of l values for which Pl(x) ...
متن کاملA discrete-time quantum walk taking continuous steps
This note introduces a quantum random walk in R and proves the weak convergence of its rescaled n-step densities. Quantum walks of the type we consider in this note were introduced in [1], which defined and analyzed the Hadamard quantum walk on Z, and a “new type of convergence theorem” for such quantum walks on Z was discovered by Konno [4, 5]. A much simpler proof of Konno’s theorem has recen...
متن کاملA Turing model with correlated random walk
If in the classical Turing model the diffusion process (Brownian motion) is replaced by a more general correlated random walk, then the parameters describing spatial spread are the particle speeds and the rates of change in direction. As in the Turing model, a spatially constant equilibrium can become unstable if the different species have different turning rates and different speeds. Furthermo...
متن کاملA Random Walk with Exponential Travel Times
Consider the random walk among N places with N(N - 1)/2 transports. We attach an exponential random variable Xij to each transport between places Pi and Pj and take these random variables mutually independent. If transports are possible or impossible independently with probability p and 1-p, respectively, then we give a lower bound for the distribution function of the smallest path at point log...
متن کاملContinuous-time correlated random walk model for animal telemetry data.
We propose a continuous-time version of the correlated random walk model for animal telemetry data. The continuous-time formulation allows data that have been nonuniformly collected over time to be modeled without subsampling, interpolation, or aggregation to obtain a set of locations uniformly spaced in time. The model is derived from a continuous-time Ornstein-Uhlenbeck velocity process that ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Statistical Mechanics: Theory and Experiment
سال: 2020
ISSN: 1742-5468
DOI: 10.1088/1742-5468/ab6a07