3 problems

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Erbar–Fathi concentration-to-spectral-gap conjecture
Erbar–Fathi conjecture. The concentration assumption implies
Conjectureopenconcentration-of-measure ollivier-curvature spectral-gaparXiv posted 2 days ago
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Pedrotti's conjecture on Ollivier curvature and modified log-Sobolev inequalities
Pedrotti's conjecture. Positive Ollivier curvature, together with non-negative $\ell_\infty$ Wasserstein curvature, implies a modified log-Sobolev inequality.
Conjectureopenlog-sobolev-inequalities ollivier-curvature wasserstein-geometryarXiv posted 2 days ago
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Tetali–Peres conjecture on Ollivier curvature and modified log-Sobolev inequalities
Tetali–Peres conjecture. Lower Ollivier curvature bounds imply modified log-Sobolev inequalities.
Conjectureopenlog-sobolev-inequalities markov-chains ollivier-curvaturearXiv posted 2 days ago

Erbar–Fathi concentration-to-spectral-gap conjecture