# Arrivals are universal in coalescing ballistic annihilation

@inproceedings{Padro2022ArrivalsAU, title={Arrivals are universal in coalescing ballistic annihilation}, author={Dar'io Cruzado Padr'o and Matthew Junge and Lily Reeves}, year={2022} }

. Coalescing ballistic annihilation is an interacting particle system intended to model features of certain chemical reactions. Particles are placed with independent and identically distributed spacings on the real line and begin moving with velocities sampled from − 1 , 0 , and 1. Collisions result in either coalescence or mutual annihilation. For a variety of symmetric coalescing rules, we prove that the index of the ﬁrst particle to arrive at the origin does not depend on the law for…

## References

SHOWING 1-10 OF 13 REFERENCES

### The phase structure of asymmetric ballistic annihilation

- Physics
- 2018

In ballistic annihilation, particles are placed throughout the real line with independent spacings and each is assigned a velocity. The particles then move at their assigned velocity and annihilate…

### Stochastic ballistic annihilation and coalescence

- PhysicsPhysical review letters
- 2000

An exact solution for the density is obtained which reveals a universal phase diagram for the asymptotic density decay and reveals two new phases, one of which contain the previously studied cases of ballistic annihilation.

### On Some Annihilating and Coalescing Systems

- Mathematics
- 1998

In the present paper we continue the investigation of the so-called coalescing ideal gas in one dimension, initiated by Ermakov. The model consists of point-like particles moving with velocities ±1…

### Note on a one-dimensional system of annihilating particles

- Mathematics
- 2016

We consider a system of annihilating particles where particles start from the points of a Poisson process on either the full-line or positive half-line and move at constant i.i.d. speeds until…

### The bullet problem with discrete speeds

- Physics, MathematicsElectronic Communications in Probability
- 2019

Bullets are fired, one per second, with independent speeds sampled uniformly from a discrete set. Collisions result in mutual annihilation. We show that the second fastest bullet survives with…

### Particle–antiparticle annihilation in diffusive motion

- Physics
- 1983

We study both numerically and analytically the time development of a system of particles and antiparticles moving diffusively and annihilating irreversibly. The asymptotic behavior is found to depend…

### Three-speed ballistic annihilation: phase transition and universality

- PhysicsSelecta Mathematica
- 2021

We consider ballistic annihilation, a model for chemical reactions first introduced in the 1980’s physics literature. In this particle system, initial locations are given by a renewal process on the…

### The upper threshold in ballistic annihilation

- PhysicsLatin American Journal of Probability and Mathematical Statistics
- 2019

Three-speed ballistic annihilation starts with infinitely many particles on the real line. Each is independently assigned either speed-$0$ with probability $p$, or speed-$\pm 1$ symmetrically with…

### The combinatorics of the colliding bullets

- MathematicsRandom Struct. Algorithms
- 2020

The finite colliding bullets problem is the following simple problem: consider a gun, whose barrel remains in a fixed direction; let (Vi)1 ≤ i ≤ n be an i.i.d. family of random variables with uniform…

### Asymptotic behavior of densities for two-particle annihilating random walks

- Mathematics
- 1991

Consider the system of particles onℤd where particles are of two types—A andB—and execute simple random walks in continuous time. Particles do not interact with their own type, but when anA-particle…