We prove a spectral gap inequality for the stochastic exchange model studied by Gaspard and Gilbert and by Grigo, Khanin and Szász in connection with understanding heat conduction in a deterministic billiards model. The bound on the spectral gap that we prove is uniform in the number of particles, as had been conjectured. We adapt techniques that were originally developed to prove spectral gap bounds for the Kac model with hard sphere collisions, which, like the stochastic exchange model, has degenerate jump rates.
Spectral gap for the stochastic exchange model / Carlen, Eric A.; Posta, Gustavo; Tóth, Imre Péter. - In: STOCHASTIC PROCESSES AND THEIR APPLICATIONS. - ISSN 0304-4149. - 190:(2025). [10.1016/j.spa.2025.104769]
Spectral gap for the stochastic exchange model
Carlen, Eric A.;Posta, Gustavo
;
2025
Abstract
We prove a spectral gap inequality for the stochastic exchange model studied by Gaspard and Gilbert and by Grigo, Khanin and Szász in connection with understanding heat conduction in a deterministic billiards model. The bound on the spectral gap that we prove is uniform in the number of particles, as had been conjectured. We adapt techniques that were originally developed to prove spectral gap bounds for the Kac model with hard sphere collisions, which, like the stochastic exchange model, has degenerate jump rates.| File | Dimensione | Formato | |
|---|---|---|---|
|
Carlen_Spectralgap_2025.pdf
accesso aperto
Tipologia:
Versione editoriale (versione pubblicata con il layout dell'editore)
Licenza:
Creative commons
Dimensione
1.13 MB
Formato
Adobe PDF
|
1.13 MB | Adobe PDF |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
