7
votes
Accepted
Randomly removing length 1 intervals in an interval (a fragmentation process)
This is exactly the so-called "Renyi parking process." Renyi proved
$$\varphi(x) = cx + c - 1 + o(1)$$
where $$c = \int_0^\infty \exp\left( -2 \int_0^x \frac{1 - e^{-y}}{y}\,dy \right)\,dx \...
- 909
2
votes
Accepted
Decay estimate of energy minimizer and the linear ODE
You can just play with the same truncation techniques you used already.
$u\ge 0$ (replace by $\max(u,0)$ on $\mathbb R$)
If $x\ge 0$ and $u(x)\ge \frac{1}{c(x)}$, then $u(y)\le u(x)$ for $y\ge x$ (...
- 59.8k
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