## Simulations for the (augmented) multiplicative coalescent

$$B_t(s) = W_t(s) - \inf_{0 \leq u \leq s} W_t(u),$$ where $W_t(s) = W(s) - \frac{1}{2}s^2 + t s$.

• $X_i(t)$: $i$th largest excursion of $B_t(\cdot)$ above zero,

• $\big( \pmb{X}(t), t \ge 0 \big)$ is a realization of an eternal multiplicative coalescent. $W_t(s) = W(s) - \frac{s^2}{2} + t s$, for $t = 0.5$ $B_t(s) = W_t(s) - \inf\limits_{0 \le u \le s} W_t(u)$, for $t = 0.5$

• $\Lambda$: homogeneous Poisson point process on $\mathbb{R}_+^2$,
• $X_i(t)$: $i$th largest excursion above zero,
• $Y_i(t)$: nb. of marks below the curve during the $i$th largest excursion.

$\big( (\pmb{X}(t), \pmb{Y}(t)), t \ge 0 \big)$ is a realization of an eternal augmented multiplicative coalescent. $B_t(s) = W_t(s) - \inf\limits_{0 \le u \le s} W_t(u)$, for $t = 0.5$
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