4 problems

Non-trivial interlacement conjecture. For every sufficiently large particle density, the minimizing point process cannot contain loops only; it must have a non-trivial interlacemen…

Interlacement-particle conjecture. The interlacement particles directly relate to, and possibly are equal to, the particles in the condensate.

ODLRO conjecture. ODLRO, and therefore BEC, is valid in dimensions $d\geq 3$ at sufficiently small temperature, but is not valid at other temperatures or in other dimensions.

Let $\chi(\rho)$ be the variational free-energy functional over shift-invariant marked point processes $P$ satisfying $P(N_U^{{{\scriptscriptstyle{({\ell}})}}})=\rho$, and let…