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Mixing Time of Conditional Two Star Exponential Random Graphs — arXiv:2609.14335

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.14335
License (as archived): CC0-1.0
Archived: 2026-10-16T01:18:45.849Z
SHA-256 of the archived text: 60051835711db13a945c034176f9b783ea0062c2ba711885d9dd4d31a1e66548
Stable URL of this page: https://metraipolis.com/documento/dc_5a69ebfc4e67

How to cite

Mixing Time of Conditional Two Star Exponential Random Graphs — arXiv:2609.14335 — arXiv (en), https://arxiv.org/abs/2609.14335 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_5a69ebfc4e67 (Metraipolis archive dc_5a69ebfc4e67, sha256 60051835711db13a945c034176f9b783ea0062c2ba711885d9dd4d31a1e66548)

BibTeX

@misc{dc5a69ebfc4e67,
  title = {Mixing Time of Conditional Two Star Exponential Random Graphs — arXiv:2609.14335},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.14335},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_5a69ebfc4e67; sha256 60051835711db13a945c034176f9b783ea0062c2ba711885d9dd4d31a1e66548},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.14335. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Two star exponential random graph models (ERGMs) are an interesting special case of both general ERGMs and mean-field Ising models. In this paper, we study two star ERGMs conditioning on the edge density $p$. We begin with an analytic characterization of the replica symmetric region, where the conditional model is close in cut distance to the Erdős--Rényi random graph $G(n,p)$. We prove that this region is twice as large as the corresponding region for the unconditional model. To study refined properties of the conditional model, we then analyze the global Kawasaki algorithm for sampling from it. Within the replica symmetric region, and under the additional condition that $4\beta p(1-p)<0.5$ when $|p-1/2|\lesssim 0.4632$, where $\beta$ is the model parameter, we prove metastable fast mixing of the Kawasaki algorithm. As corollaries, we obtain a weak Poincaré inequality and use it to deduce concentration inequalities of optimal order for conditional subgraph counts. The additional condition $4\beta p(1-p)<1/2$ if $|p-1/2|\lesssim 0.4632$ comes from our proof technique of contractive coupling. This bottleneck did not appear in previous studies applying the contractive coupling technique to unconditional ERGMs.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-15 in math.PR).
Categorie arXiv: Probability (math.PR).
Pagina del lavoro: https://arxiv.org/abs/2609.14335 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-16T00:31:28.420Z dalla pagina https://arxiv.org/catchup/math.PR/2026-09-15?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).