6 problems

Let $\operatorname{MD}_{\mathrm{coins}}$ denote the coin-valued median dynamics process on $\mathbb{Z}^d$, and let $\eta_t(\underline{0})$ be the opinion at the origin. Coin-median…

Let $\operatorname{MD}_{\mathrm{coins}}$ denote the coin-valued median dynamics process on $\mathbb{Z}^d$, and let $\eta_t(\underline{0})$ be the opinion at the origin. Coin-median…

Consider median dynamics on $\mathbb{Z}^2$, with $\eta_\infty(0)$ denoting the limiting opinion at the origin. Stable-structure tail conjecture. … The exponent $4$ comes from the s…

Let $(\eta_t)_{t\geq0}$ be median dynamics and, for an initial density $p\in[0,1]$, let $(\xi_t^p)_{t\geq0}$ be the coupled majority-dynamics process. Say that majority dynamics fi…

Let $p_t^x$ denote the density of the marginal law of the median-dynamics opinion $\eta_t(x)$ on $[0,1]$. Unimodality conjecture. The density $p_t^x$ is symmetric around $\frac12$…

Let $G$ be a graph, let $x\in G$, and let $(\eta_t)_{t\geq0}$ denote median dynamics with i.i.d. uniform initial opinions on $[0,1]$. For $\alpha\in[0,1]$, define…