Linear extrapolation for the graph of function of single variable based on walks

Abstract

The quantum walk was introduced as a quantum counterpart of the random walk and has been intensively studied since around 2000. Its applications include topological insulators, radioactive waste reduction, and quantum search. The first author in 2019 defined a time-series model based on the measure of the ``discrete-time" and ``discrete-space" quantum walk in one dimension. Inspired by his model, this paper proposes a new model for the graph of a function of a single variable determined by the measure which comes from the weak limit measure of a ``continuous-time or discrete-time" and ``discrete-space" walk. The measure corresponds to a ``continuous-time" and ``continuous-space" walk in one dimension. Moreover, we also presents a method of a linear extrapolation for the graph by our model.