clopen.solutions

Open problems

980 registered problems.

OP-00310 Open
Monotonicity of draw probabilities under random vertex deletion
PR · AIM Open Applied Problems · combinatorial games · site percolation
OP-00403 Solution claimed
Does supercritical percolation preserve transience?
PR · AIM Open Applied Problems · Cayley graphs · percolation · random walks
OP-00433 Open
The two-thirds passage-time variance exponent
PR · AIM Open Applied Problems · first-passage percolation · fluctuation exponents · KPZ universality
OP-00482 Open
Connectivity of the three-dimensional minimal spanning forest
PR · AIM Open Applied Problems · invasion percolation · minimal spanning forests
OP-00486 Open
Exclusion of coexistence for unequal Richardson growth rates
PR · AIM Open Applied Problems · competing growth · first-passage percolation · Richardson model
OP-00659 Solution claimed
Absence of doubly infinite minimizing paths in planar first-passage percolation
PR · AIM Open Applied Problems · bigeodesics · first-passage percolation
OP-00673 Solution claimed
Absence of an infinite cluster at criticality in three-dimensional percolation
PR · AIM Open Applied Problems · critical phenomena · percolation
OP-00700 Solution claimed
A nonuniqueness phase on every nonamenable transitive graph
PR · AIM Open Applied Problems · nonamenable graphs · percolation · uniqueness threshold
OP-00719 Solution claimed
Cardy's crossing formula for square-lattice bond percolation
PR · AIM Open Applied Problems · conformal invariance · critical percolation · crossing probabilities
OP-00725 Solution claimed
Strict convexity of the planar exponential first-passage shape
PR · AIM Open Applied Problems · first-passage percolation · limit shapes
OP-00775 Solution claimed
Draws in the undirected trapping game on percolation clusters
PR · AIM Open Applied Problems · combinatorial games · site percolation
OP-00864 Open
A strict gap between face and cycle percolation thresholds
PR · AIM Open Applied Problems · continuum percolation · random simplicial complexes