# Large deviations of the ballistic Lévy walk model.

@article{Wang2020LargeDO, title={Large deviations of the ballistic L{\'e}vy walk model.}, author={Wanli Wang and Marc H{\"o}ll and Eli Barkai}, journal={Physical review. E}, year={2020}, volume={102 5-1}, pages={ 052115 } }

We study the ballistic Lévy walk stemming from an infinite mean traveling time between collision events. Our study focuses on the density of spreading particles all starting from a common origin, which is limited by a "light" cone -v_{0}t<x<v_{0}t. In particular we study this density close to its maximum in the vicinity of the light cone. The spreading density follows the Lamperti-arcsine law describing typical fluctuations. However, this law blows up in the vicinity of the spreading horizon…

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## References

SHOWING 1-10 OF 78 REFERENCES

### Power‐Law Blinking Quantum Dots: Stochastic and Physical Models

- Physics
- 2005

We quantify nonergodic and aging behaviors of nanocrystals (or quantum dots) based on stochastic model. Ergodicity breaking is characterized based on time average intensity and time average…

### First Steps in Random Walks: From Tools to Applications

- Mathematics, Physics
- 2011

1. Characteristic Functions 2. Generating Functions and Applications 3. Continuous Time Random Walks 4. CTRW and Aging Phenomena 5. Master Equations 6. Fractional Diffusion and Fokker-Planck…

### An introduction to infinite ergodic theory

- Mathematics
- 1997

Non-singular transformations General ergodic and spectral theorems Transformations with infinite invariant measures Markov maps Recurrent events and similarity of Markov shifts Inner functions…

### Fractional Differential Equations (Academic Press, Inc

- San Diego,
- 1999

### An Introduction to Probability Theory and Its Applications

- Mathematics
- 1950

Thank you for reading an introduction to probability theory and its applications vol 2. As you may know, people have look numerous times for their favorite novels like this an introduction to…

### Distribution with a simple Laplace transform and its applications to non-Poissonian stochastic processes

- MathematicsJournal of Statistical Mechanics: Theory and Experiment
- 2020

In this paper, we propose a novel probability distribution that asymptotically represents a power-law, ψ(t) ∼ t−α−1, with 0 < α < 2. The main feature of the distribution is that it has a simple…

### Extreme value theory for constrained physical systems.

- MathematicsPhysical review. E
- 2020

In the thermodynamic limit, the theory is shown how it is suitable to describe typical and rare events which deviate from classical extreme value theory, and dual scaling of the extreme value distribution is unraveled.

### Rare events in generalized Lévy Walks and the Big Jump principle

- MathematicsScientific Reports
- 2020

This work derives the bulk of the probability distribution and uses the big jump principle, the exact form of the tails that describes rare events, and shows that the tails of the distribution present non-universal and non-analytic behaviors, which depend crucially on the dynamics of the single step.

### Infinite invariant density in a semi-Markov process with continuous state variables.

- MathematicsPhysical review. E
- 2020

It is shown that the infinite invariant density plays an important role in determining the distribution of time averages, and two scaling laws describing the density for the state value are found, which accumulates in the vicinity of zero in the long-time limit.

### Age representation of Lévy walks: partial density waves, relaxation and first passage time statistics

- MathematicsJournal of Physics A: Mathematical and Theoretical
- 2019

Lévy walks (LWs) define a fundamental class of finite velocity stochastic processes that can be introduced as a special case of continuous time random walks. Alternatively, there is a hyperbolic…