Average trajectory of returning walks

Average persistence of random walks

– We study the first passage time properties of an integrated Brownian curve both in homogeneous and disordered environments. In a disordered medium we relate the scaling properties of this center-of-mass persistence of a random walker to the average persistence, the latter being the probability Ppr(t) that the expectation value 〈x(t)〉 of the walker’s position after time t has not returned to t...

Classification on the average of random walks

We introduce a new method for studying large scale properties of random walks. The new concepts of transience and recurrence on the average are compared with the ones introduced in [1] and with the usual ones; their relationships are analyzed and various examples are provided.

Average mixing of continuous quantum walks

Average Multiplicity , Secondary Trajectory , and Mueller Analysis

The correction to the average multiplicity is calculated in a general Mueller analysis when a secondary Regge trajectory with intercept l/2 is also included. is then approximately given by [ APn s + B + C s -l/2 3 , which fits well all existing multiplicity data from s = 25 GeV2 to 2800 GeV’. We show that part of the coefficient C may be estimated from the 90’ production data. We comment on...

Random Walks in Random Environment: What a Single Trajectory Tells

We present a procedure that determines the law of a random walk in an iid random environment as a function of a single “typical” trajectory. We indicate when the trajectory characterizes the law of the environment, and we say how this law can be determined. We then show how independent trajectories having the distribution of the original walk can be generated as functions of the single observed...