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Ban, Jung-Chao; Hu, Wen-Guei; Lai, Guan-Yu

doi:10.1016/j.indag.2021.09.010

Cited by 3 publications

(1 citation statement)

References 13 publications

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“…2. The proof is similar to the (2) of Theorem 3.2 in [2]. More pricisely, we are going to show the sum…”

Section: The Multiple Averagementioning

confidence: 76%

Thermodynamic formalism and large deviation principle of multiplicative Ising models

Ban¹,

Hu²,

Lai³

2022

Preprint

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The aim of this study is tree-fold. First, we investigate the thermodynamics of the Ising models with respect to 2-multiple Hamiltonians. This extends the previous results of [Chazotte and Redig, Electron. J. Probably., 2014] to N d . Second, we establish the large deviation principle (LDP) of the average 1 N S G N , where S G N is a 2-multiple sum along a semigroup generated by k numbers which are k co-primes. This extends the previous results [Ban et al. Indag. Math., 2021] to a board class of the long-range interactions. Finally, the results described above are generalized to the multidimensional lattice N d , d ≥ 1.

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“…2. The proof is similar to the (2) of Theorem 3.2 in [2]. More pricisely, we are going to show the sum…”

Section: The Multiple Averagementioning

confidence: 76%

Thermodynamic formalism and large deviation principle of multiplicative Ising models

Ban¹,

Hu²,

Lai³

2022

Preprint

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Hausdorff dimension of multidimensional multiplicative subshifts

Ban

Hu²,

Lai

2023

Ergod. Th. Dynam. Sys.

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The purpose of this study is two-fold. First, the Hausdorff dimension formula of the multidimensional multiplicative subshift (MMS) in $\mathbb {N}^d$ is presented. This extends the earlier work of Kenyon et al [Hausdorff dimension for fractals invariant under multiplicative integers. Ergod. Th. & Dynam. Sys.32(5) (2012), 1567–1584] from $\mathbb {N}$ to $\mathbb {N}^d$ . In addition, the preceding work of the Minkowski dimension of the MMS in $\mathbb {N}^d$ is applied to show that their Hausdorff dimension is strictly less than the Minkowski dimension. Second, the same technique allows us to investigate the multifractal analysis of multiple ergodic average in $\mathbb {N}^d$ . Precisely, we extend the result of Fan et al, [Multifractal analysis of some multiple ergodic averages. Adv. Math.295 (2016), 271–333] of the multifractal analysis of multiple ergodic average from $\mathbb {N}$ to $\mathbb {N}^d$ .

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Boundary complexity and surface entropy of 2-multiplicative integer systems on Nd

Ban

Lai

2023

Journal of Mathematical Physics

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In this article, we introduce the concept of boundary complexity and prove that for a 2-multiplicative integer system (2-MIS) XΩp on N (or XΩp on Nd,d≥2), every point in [h(XΩp),log⁡r] can be realized as a boundary complexity of a 2-MIS at a specific speed, where r stands for the size of the alphabet. The result is new and quite different from the Nd subshift of finite type (SFT) for d ≥ 1. Furthermore, the formula of surface entropy for a Nd 2-MIS is also presented. This illustrates an efficient method to calculate the topological entropy for Nd 2-MIS and also provides intrinsic differences between Ndk-MIS and SFTs for d ≥ 1 and k ≥ 2.

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Large deviation principle of multidimensional multiple averages on Nd

Cited by 3 publications

References 13 publications

Thermodynamic formalism and large deviation principle of multiplicative Ising models

Thermodynamic formalism and large deviation principle of multiplicative Ising models

Hausdorff dimension of multidimensional multiplicative subshifts

Boundary complexity and surface entropy of 2-multiplicative integer systems on Nd

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