18 problems

Krapivsky–Redner–Leyvraz conjecture. The critical probability is

Critical-speed conjecture. There is a critical speed $s_c\in(0,1)$ such that the first bullet survives with positive probability if and only if its speed is greater than $s_c$.

Let $\nu$ be the distribution of the sizes of arrow clusters, and let $p_c$ denote the critical initial density for fixation in the clustered ballistic annihilation model. In line…

Critical-point conjecture. For each $n$, the function $p\mapsto\frac{2}{1-p}p_n$ is maximized at $p=1/4$.

Monotonicity conjecture. For each $n$, the function $p\mapsto p_n$ is monotonically decreasing on $[1/4,1]$.

Monotonicity conjecture. The law of $A$ is affected monotonically by changing $p$.

In the asymmetric three-velocity ballistic annihilation model, let $p$ and $\lambda$ be the model parameters, let $\vec{\alpha}$, $\cev{\alpha}$, and $\hat{\alpha}$ be the one-side…

Consider asymmetric three-velocity ballistic annihilation with unit spacings, so that $\mu=\delta_1$, and let $p$ denote the relevant particle-density parameter and $\lambda$ the a…

In ballistic annihilation, particles are placed on the real line with independent spacings distributed according to a probability measure $\mu$ having no mass at $0$ and finite mea…

For the continuous ballistic annihilation process, define $\theta(p)$ as the probability that a stationary particle survives forever, and set … For the discretised process, define…

In the discretised ballistic annihilation process, one particle starts at every integer point, each particle is stationary with probability $p$ and moves at unit speed left or righ…

Consider ballistic annihilation with an inert particle at the origin and particles at the positive integers, whose speeds are independently sampled from the three-speed distributio…

In three-speed ballistic annihilation, particles on the real line independently have speed $0$ with probability $p$ and speed $71$ with the remaining probability, with all particle…

Trizac's mass-decay conjecture. The mass behaves in the long run as

Consider ballistic annihilation on $\mathbb{Z}$: each site is initially a particle with probability $p$ and a blockade with probability $1-p$, independently; each particle is indep…

Consider particles released from the origin at the points of a Poisson point process, with independent and identically distributed positive velocities $(w_k)_{k\geq 1}$, which anni…

Conditioned exponent conjecture. There is an exponent $c_s$ such that

Critical-speed conjecture. The critical speed satisfies