TASEP Diffusion Coefficients from Weak Asymmetry Limits

Definitions and mathematical statement

The supplied record concerns a velocity-exclusion model and its proposed relation to the totally asymmetric simple exclusion process (TASEP). Let $d$ denote the spatial dimension. The record uses $D_\gamma(1)$, with a positive parameter $\gamma$ tending to zero, but does not define the model, the coefficient $D_\gamma$, or the meaning of its argument $1$.

The reported conjectural question is whether the limit \[ \lim_{\gamma\downarrow 0}D_\gamma(1) \] determines, or otherwise relates to, the TASEP diffusion coefficient. The supplied formulation describes that TASEP coefficient as divergent for $d=1,2$ and finite for $d\geq 3$. These dimensional assertions are part of the supplied formulation, not independently verified facts in this draft. The background specifically describes the target as a high-dimensional velocity-exclusion asymptotic and a proposed relation to the TASEP diffusion coefficient.

The existence and possible finiteness of the displayed limit are not specified. Neither the precise TASEP coefficient nor the proposed relation is defined: the record gives no equality, normalization, scaling prescription, or other mathematical criterion for "determines" or "relates to." Consequently, the supplied evidence supports this qualified question but does not determine a precise conjectural identity or a fully specified mathematical proposition.

Short English statement

The question asks whether a small-$\gamma$ limit of a velocity-exclusion coefficient describes a TASEP diffusion coefficient. The supplied record states a divergence/finite distinction between dimensions $1,2$ and dimensions at least $3$, but leaves the coefficients, model parameters, and proposed relation unspecified. A precise formulation requires these missing definitions.

Sources

• Local UnsolvedMath registry, supplied complete record: permanent ID $30001620$, source problem code catalogue entry, title "TASEP Diffusion Coefficients from Weak Asymmetry Limits." The supplied proposed year is 2010; no proposer is named.
• Supplied source citation: Large Scale Stochastic Dynamics (2011), Oberwolfach Reports, pp. 2877--2975, DOI 10.4171/owr/2010/50. Original report and supplied literature-source link: https://doi.org/10.4171/owr/2010/50. The background describes Oberwolfach Reports as documenting mathematical workshops and their open-problem discussions.
• Supplied literature source: "Sasada, velocity exclusion hydrodynamics," https://math-mprf.org/journal/articles/id1246/. No fuller bibliographic details or supporting passage are supplied.
• Literature assessment dated 2026-08-21: the supplied curation labels the problem open and says that the high-dimensional velocity-exclusion asymptotic and its proposed relation to the TASEP diffusion coefficient were conjectural, with the checked literature not establishing the exact limit relation. This is supplied dated curation, not an independently verified literature assessment; the record itself requests independent verification of time-sensitive status and cited claims.