The exclusion process mixes (almost) faster than independent particles
Why this work is in the frame
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Bibliographic record
Abstract
Oliveira conjectured that the order of the mixing time of the exclusion process with $k$-particles on an arbitrary $n$-vertex graph is at most that of the mixing-time of $k$ independent particles. We verify this up to a constant factor for $d$-regular graphs when each edge rings at rate $1/d$ in various cases: (1) when $d=\Omega (\log _{n/k}n)$, (2) when $\mathrm{gap}:=$ the spectral-gap of a single walk is $O(1/\log ^{4}n)$ and $k\ge n^{\Omega (1)}$, (3) when $k\asymp n^{a}$ for some constant $0<a<1$. In these cases, our analysis yields a probabilistic proof of a weaker version of Aldous’ famous spectral-gap conjecture (resolved by Caputo et al.). We also prove a general bound of $O(\log n\log \log n/\mathrm{gap})$, which is within a $\log \log n$ factor from Oliveira’s conjecture when $k\ge n^{\Omega (1)}$. As applications, we get new mixing bounds: (a) $O(\log n\log \log n)$ for expanders, (b) order $d\log (dk)$ for the hypercube $\{0,1\}^{d}$, (c) order $(\mathrm{Diameter})^{2}\log k$ for vertex-transitive graphs of moderate growth and for supercritical percolation on a fixed dimensional torus.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.007 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it