# Exact recovery in block spin Ising models at the critical line

@article{Lowe2019ExactRI, title={Exact recovery in block spin Ising models at the critical line}, author={Matthias Lowe and Kristina Schubert}, journal={arXiv: Probability}, year={2019} }

We show how to exactly reconstruct the block structure at the critical line in the so-called Ising block model. This model was re-introduced by Berthet, Rigollet and Srivastava in a recent paper. There the authors show how to exactly reconstruct blocks away from the critical line and they give an upper and a lower bound on the number of observations one needs; thereby they establish a minimax optimal rate (up to constants). Our technique relies on a combination of their methods with fluctuation…

## 4 Citations

Large deviations and a phase transition in the Block Spin Potts models.

- Mathematics
- 2020

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…

Fluctuations of the magnetization in the Block Potts Model

- Mathematics, Physics
- 2021

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…

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

- Mathematics
- 2021

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…

Cutoff and Dynamical Phase Transition for the General Multi-component Ising Model

- Mathematics, Physics
- 2021

We study the multi-component Ising model, which is also known as the block Ising model. In this model, the particles are partitioned into a fixed number of groups with a fixed proportion, and the…

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