7 problems

Let $G$ be the evolving random graph process, and write $\tau(\mathcal E)$ for the hitting time at which event $\mathcal E$ first occurs. Let ${\cal M}$ be the perfect matching gam…

Let $n\equiv 1,3 \pmod 6$, and let $T_1,T_2,\ldots$ be a uniformly random ordering of the triples in $\binom{[n]}{3}$. Steiner triple system hitting-time conjecture. With high prob…

Distributional-limit conjecture. If $\kappa\in(2,3)$, then

Let $K_k^n$ be the complete $k$-uniform hypergraph on $n$ vertices, and expose its edges one by one in a uniformly random order to obtain the random hypergraph process. A facet is…

Let $K_k^n$ be the complete $k$-uniform hypergraph on $n$ vertices, and expose its edges one by one in a uniformly random order to obtain the random hypergraph process. A facet is…

Let $X$ be a Markov chain with finite state space $S$, where $|S|=n$, and let $x$ and $y$ be any two states. Holroyd's interval hitting-time conjecture. For all $t>n$, … This conje…

Let $X$ be a reversible Markov chain with finite state space, and let $\pi$ be the stationary distribution of $X$. For states $x$ and $y$, write $\tau(y)$ for the hitting time of…