# Questions tagged [gibbs-measure]

Questions on the Gibbs measure in any measurable space $(\mathbb{E}^\mathbb{T},\mathcal{F})$ defined by a family of potentials $\Phi=\{\Phi_t\}_{t\in\mathbb{T}}$ in a net $\mathbb{T}$. Here $\mathbb{E}$ is a topological space or a measurable space.

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### Ising Model using morphological filters

How can i prove that a simple MRF of some interest in image processing and analysis is the Ising model, whose energy function is: $U(X)=a|X|+b_{1}|(X \ominus B_{1})|+b_{2}|(X \ominus B_{2})|$ when we ...
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### Negative Log-Likelihood Loss with Gibbs distribution for beta approaching infinity

TL;DR: What happens with Gibb's distribution when $\beta \to \infty$ and why? $$\lim_{\beta \to \infty} \frac{\exp(-\beta E(W, Y^i, X^i))}{\int_y \exp(-\beta E(W, y, X^i)) } \ = \ ?$$ Full ...
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### Compute transition probabilities for reversible dynamics wrt Gibbs measure

I'm looking at this paper about Gibbs measure on random graph. I don't understand how to compute transition probabilities for the first example (known as Glauber or Metropolis dynamics, pag 4-5) for ...
189 views

### Uniqueness of Gibbs measure for rotator model in one dimension

I am trying to solve a problem in a course of Y. Velenik (models with continuous symmetry, exercice 8.18: http://www.unige.ch/math/folks/velenik/smbook/index.html): Show that in dimension $d=1$ ...
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### Ising Model on 2k-regular graphs

Is Ising model on any infinite $2k$-regular graph (where the vertex degree is exactly $2k$) equal to Ising model on $\mathbb{Z}^k$ ($\mathbb{Z}^k$ lattice) ( where the vertex degree is $2k$ as well ...
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### How to Derive Gibbs Sampling Update Formula for Hidden Markov Model?

I want to understand how to derive the update formula for Gibbs sampling for Hidden Markov Model, for example, in here: p(z_t | \mathbf{x}, \mathbf{z}_{\setminus t}, \boldsymbol{\alpha}, > \...