Cutoff conjecture for symmetric simple exclusion with open boundaries

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Let p=12p=\frac{1}{2} and let α,β,γ,δ≥0\alpha,\beta,\gamma,\delta\geq 0 satisfy

max⁡(α,γ)>0,max⁡(β,δ)>0.\max(\alpha,\gamma)>0,\qquad \max(\beta,\delta)>0.

Symmetric cutoff conjecture. The lower bound in the symmetric pre-cutoff estimate is sharp, and cutoff occurs.

This conjecture concerns the mixing behavior of the symmetric simple exclusion process with two open boundaries, viewed heuristically as a symmetric exclusion process on a circle. The source gives no resolution of the conjecture.

References

Primary source

Nina Gantert, Evita Nestoridi and Dominik Schmid, “Mixing times for the simple exclusion process with open boundaries”, arXiv:2003.03781 (2022).

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