Exact recovery in block spin Ising models at the critical line

Löwe, Matthias; Schubert, Kristina

doi:10.1214/20-ejs1703

Cited by 6 publications

(5 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In particular they were discussed as models for social interactions between several groups, e. g. in [16,2,34,32] (the latter paper studies a combination of Ising models on Erdös-Rényi graphs as in [7,21,22] and block models). Recently, block models have also been studied in a statistical context (see [3], [31]). Here the task is to exactly recover the block structure from a given number of realizations of the model.…”

Section: Introductionmentioning

confidence: 99%

Large deviations, a phase transition, and logarithmic Sobolev inequalities in the block spin Potts model

Knöpfel

Löwe

Sambale

2021

Electron. Commun. Probab.

Self Cite

View full text Add to dashboard Cite

We introduce and analyze a generalization of the blocks spin Ising (Curie-Weiss) models that were discussed in a number of recent articles. In these block spin models each spin in one of s blocks can take one of a finite number of q ≥ 3 values or colors, hence the name block spin Potts model. We prove a large deviation principle for the percentage of spins of a certain color in a certain block. These values are represented in an s × q matrix. We show that for uniform block sizes there is a phase transition. In some regime the only equilibrium is the uniform distribution of all colors in all blocks, while in other parameter regimes there is one predominant color, and this is the same color with the same frequency for all blocks. Finally, we establish log-Sobolev-type inequalities for the block spin Potts model.

show abstract

Section: Introductionmentioning

confidence: 99%

Large deviations, a phase transition, and logarithmic Sobolev inequalities in the block spin Potts model

Knöpfel

Löwe

Sambale

2021

Electron. Commun. Probab.

Self Cite

View full text Add to dashboard Cite

show abstract

“…These block spin models were investigated in a number of papers, from both a static and a dynamic point of view, see [3,[12][13][14]17,18,20,23,25]. Statistical questions in block spin models were studied in [2] and [24]. All the above papers, however, discuss the situation where each spin only takes two values, hence generalized mean-field Ising models or Curie-Weiss models.…”

Section: Introductionmentioning

confidence: 99%

Fluctuations of the Magnetization in the Block Potts Model

2022

Self Cite

View full text Add to dashboard Cite

In this note we study the block spin mean-field Potts model, in which the spins are divided into s blocks and can take $$q\ge 2$$ q ≥ 2 different values (colors). Each block is allowed to contain a different proportion of vertices and behaves itself like a mean-field Ising/Potts model which also interacts with other blocks according to different temperatures. Of particular interest is the behavior of the magnetization, which counts the number of colors appearing in the distinct blocks. We prove central limit theorems for the magnetization in the generalized high-temperature regime and provide a moderate deviation principle for its fluctuations on lower scalings. More precisely, the magnetization concentrates around the uniform vector of all colors with an explicit, but singular, Gaussian distribution. In order to remove the singular component, we will also consider a rotated magnetization, which enables us to compare our results to various related models.

show abstract

“…These block spin models were investigated in a number of papers, from both a static and a dynamic point of view, see [GC08], [GBC09], [FC11], [Col14], [LS18], [LSV20], [KLSS20], [KT20b], [KT20a]. Statistical questions in block spins models were studied in [BRS19] and [LS20]. All the above papers, however, discuss the situation where each spin only takes two values, hence generalized mean-field Ising models or Curie-Weiss models.…”

Section: Introductionmentioning

confidence: 99%

Fluctuations of the magnetization in the Block Potts Model

Jalowy,

Löwe,

Sambale

2021

Preprint

Self Cite

View full text Add to dashboard Cite

In this note we study the block spin mean-field Potts model, in which the spins are divided into s blocks and can take q ≥ 2 different values (colors). Each block is allowed to contain a different proportion of vertices and behaves itself like a mean-field Ising/Potts model which also interacts with other blocks according to different temperatures. Of particular interest is the behavior of the magnetization, which counts the number of colors appearing in the distinct blocks. We prove central limit theorems for the magnetization in the generalized high temperature regime and provide a moderate deviation principle for its fluctuations on lower scalings. More precisely, the magnetization concentrates around the uniform vector of all colors with an explicit, but singular, Gaussian distribution. In order to remove the singular component, we will also consider a rotated magnetization, which enables us to compare our results to various related models.

show abstract

Exact recovery in block spin Ising models at the critical line

Cited by 6 publications

References 27 publications

Large deviations, a phase transition, and logarithmic Sobolev inequalities in the block spin Potts model

Large deviations, a phase transition, and logarithmic Sobolev inequalities in the block spin Potts model

Fluctuations of the Magnetization in the Block Potts Model

Fluctuations of the magnetization in the Block Potts Model

Contact Info

Product

Resources

About