2 problems

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The growth-rate conjecture for dielectric-breakdown models
Growth-rate conjecture. For every $\eta>0$ , the limit defining $\beta(\eta)$ exists almost surely and is nontrivial.
Conjectureopendielectric-breakdown-model stochastic-growtharXiv posted 2 days ago
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The conjecture that DBM produces irregular clusters
Irregular-cluster conjecture. DBM also produces irregular clusters in a similar manner to DLA.
Conjectureopendielectric-breakdown-model diffusion-limited-aggregation stochastic-growtharXiv posted 2 days ago

The growth-rate conjecture for dielectric-breakdown models