Planar nearest-neighbor first-passage percolation with iid nonnegative nonatomic edge weights almost surely has no doubly infinite geodesic when the minimum of four independent weights has finite second moment.
Planar nearest-neighbor first-passage percolation with iid nonnegative nonatomic edge weights almost surely has no doubly infinite geodesic when the minimum of four independent weights has finite second moment.
Planar nearest-neighbor first-passage percolation with iid nonnegative nonatomic edge weights almost surely has no doubly infinite geodesic when the minimum of four independent weights has finite second moment.
If correct, resolves the planar no-bigeodesics conjecture under the stated moment condition.
Are all bigeodesics absent in planar first-passage percolation under continuous weights?
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OpenAI reports no bigeodesics in planar first-passage percolation
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