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Bayesian Tracking of a Diffusing Target in Two and Three Dimensions — arXiv:2609.00144

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.00144
License (as archived): CC0-1.0
Archived: 2026-10-17T07:21:02.802Z
SHA-256 of the archived text: 94eaaa650b48d317b71c70cf5279d63b925b6af668084a9f3763a1194dca1ab5
Stable URL of this page: https://metraipolis.com/documento/dc_43648bc0ddda

How to cite

Bayesian Tracking of a Diffusing Target in Two and Three Dimensions — arXiv:2609.00144 — arXiv (en), https://arxiv.org/abs/2609.00144 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_43648bc0ddda (Metraipolis archive dc_43648bc0ddda, sha256 94eaaa650b48d317b71c70cf5279d63b925b6af668084a9f3763a1194dca1ab5)

BibTeX

@misc{dc43648bc0ddda,
  title = {Bayesian Tracking of a Diffusing Target in Two and Three Dimensions — arXiv:2609.00144},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.00144},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_43648bc0ddda; sha256 94eaaa650b48d317b71c70cf5279d63b925b6af668084a9f3763a1194dca1ab5},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.00144. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We study Bayesian tracking of a diffusing target monitored by a noisy distributed sensor array. Building on an earlier mapping to KPZ growth with a moving defect (or an equivalent directed polymer pinning problem) we determine the phase structure, beyond the previously-studied one-dimensional case, for both Bayes-optimal and suboptimal inference. In $d=2$, theoretical analysis and numerical simulations both give a depinning transition between a successful tracking phase and a failure phase. Weak-coupling RG shows that Bayes-optimal tracking is always successful in $d=2$, but failure can arise from overconfident (suboptimal) inference. In $d=3$, tracking can succeed, or can fail in two distinct ways: the posterior probability distribution may delocalize (no detection), or may become sharply localized, but at the wrong position (a false detection). The two possibilities correspond to Edwards-Wilkinson or Kardar-Parisi-Zhang statistics for the log-posterior. The three phases meet at a Nishimori-like multicritical point on a Bayes-optimal line in a two-parameter phase diagram. (Model misspecification alone can drive depinning into either unpinned phase: underconfidence gives diffuse failure, while overconfidence gives localized-but-wrong failure.) We analyze the transitions between the various phases numerically and with renormalization group arguments. We show that some of these have unusual critical behavior, which the conventional $\epsilon$ expansion fails to describe. Recent rigorous results for directed polymers indicate an alternative scenario. Many of our results, including a scaling relation for exponents at pinning transitions and results for RG flows, are relevant to other phase transitions that involve surface growth or directed polymers in 2+1D or 3+1D.

Tema degli esploratori: fisica e astronomia (retro-catalogo arXiv: annunci del 2026-09-02 in cond-mat.stat-mech).
Categorie arXiv: Statistical Mechanics (cond-mat.stat-mech) ; Disordered Systems and Neural Networks (cond-mat.dis-nn); Soft Condensed Matter (cond-mat.soft).
Pagina del lavoro: https://arxiv.org/abs/2609.00144 — 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 2026-10-17T07:14:32.195Z dalla pagina https://arxiv.org/catchup/cond-mat.stat-mech/2026-09-02?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).