# A weak limit theorem for a class of long range type quantum walks in 1d

## TL;DR

This paper establishes a weak limit theorem for a specific class of long-range quantum walks in one dimension, analyzing spectral properties and proving the existence and completeness of modified wave operators.

## Contribution

It introduces a weak limit theorem for long-range quantum walks and demonstrates the existence and completeness of modified wave operators for this class.

## Key findings

- Weak limit theorem established for long-range quantum walks in 1D
- Spectral analysis confirms properties of the time evolution operator
- Existence and completeness of modified wave operators proven

## Abstract

We derive the weak limit theorem for a class of long range type quantum walks. To do it, we analyze spectral properties of a time evolution operator and prove that modified wave operators exist and are complete.