Central Limit Theorem and Large Deviation Principle for Continuous Time Open Quantum Walks

Quantum central limit theorem for continuous-time quantum walks on odd graphs

The method of spectral distribution only requires simple structural data of graph and allows us to avoid a heavy combinational argument often necessary to obtain full description of spectrum of the adjacency matrix. The idea of calculation of the probability amplitudes for continuous-time quantum walk, in terms of the spectral distribution associated with the adjacency matrix of graphs was firs...

Central Limit Theorems for Open Quantum Random Walks∗

Open Quantum Random Walks, as developed in [1], are the exact quantum generalization of Markov chains on finite graphs or on nets. These random walks are typically quantum in their behavior, step by step, but they seem to show up a rather classical asymptotic behavior, as opposed to the quantum random walks usually considered in Quantum Information Theory (such as the well-known Hadamard random...

A Large Deviation Rate and Central Limit Theorem for Horton Ratios

Limit Theorem for Continuous-time Random Walks with Two Time Scales

Continuous-time random walks incorporate a random waiting time between random jumps. They are used in physics tomodel particle motion. A physically realistic rescaling uses two different time scales for the mean waiting time and the deviation from the mean. This paper derives the scaling limits for such processes. These limit processes are governed by fractional partial differential equations t...

Central Limit Theorem for Branching Random Walks in Random Environment

We consider branching random walks in d-dimensional integer lattice with time-space i.i.d. offspring distributions. When d ≥ 3 and the fluctuation of the environment is well moderated by the random walk, we prove a central limit theorem for the density of the population, together with upper bounds for the density of the most populated site and the replica overlap. We also discuss the phase tran...