For d>1, smooth solutions of the CBO Fokker-Planck equation are positive away from the consensus point, so the usual initial-support condition for global convergence can be dropped.
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Regularity and positivity of solutions of the Consensus-Based Optimization equation: unconditional global convergence
For d>1, smooth solutions of the CBO Fokker-Planck equation are positive away from the consensus point, so the usual initial-support condition for global convergence can be dropped.