Abstract
Dyson’s model in infinite dimensions is a system of Brownian particles interacting via a logarithmic potential with an inverse temperature of \( \beta = 2\). The stochastic process is given as a solution to an infinite-dimensional stochastic differential equation. Additionally, a Dirichlet form with the sine\( _2\) point process as a reference measure constructs the stochastic process as a functional of the associated configuration-valued diffusion process. In this paper, we prove that Dyson’s model in infinite dimensions is irreducible.
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Acknowledgements
This work was supported by JSPS KAKENHI Grant Numbers JP16H06338, JP20K20885, JP21H04432, and JP18H03672. We thank Stuart Jenkinson, Ph.D., from Edanz Group (https://jpen-author-services.edanz.com/ac) for editing a draft of this manuscript.
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Osada, H., Tsuboi, R. (2022). Dyson’s Model in Infinite Dimensions Is Irreducible. In: Chen, ZQ., Takeda, M., Uemura, T. (eds) Dirichlet Forms and Related Topics. IWDFRT 2022. Springer Proceedings in Mathematics & Statistics, vol 394. Springer, Singapore. https://doi.org/10.1007/978-981-19-4672-1_21
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DOI: https://doi.org/10.1007/978-981-19-4672-1_21
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