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In probability and statistics, a probability distribution assigns a probability to each measurable subset of the possible outcomes of a random experiment, survey, or procedure of statistical inference.

5 votes
1 answer
519 views

Reference Request for a particular approach of (rigorous) statistical mechanics

I was reading Mathematical Aspects of Quantum Field Theory by. E. de Faria and W. de Melo, and the following caught my attention. In (Hamiltonian) mechanics, the states of a system are described by p …
2 votes
1 answer
159 views

Expected value of global functions in renormalization group

This is related to my previous question. I'm having some problems understanding the local to global program discussed in Brydge's lecture notes. We are assuming $C=C_{1}+\cdots+C_{N}$ is a covariance …
4 votes
2 answers
263 views

Grand-canonical Gibbs measure for continuous systems

Let's consider a bounded (maybe compact) set $\Lambda \subset \mathbb{R}^{d}$ with particles interacting on it. Suppose, for each $N \in \mathbb{N}$, $U_{N}: (\mathbb{R}^{d})^{N} \to \mathbb{R}\cup \{ …
0 votes
1 answer
84 views

Renormalization group map on hierarchical models

I have already addressed this problem on my previous question but I still have trouble understanding Brydges' RG maps on his lecture notes, so I'll try to elaborate my question a little better. Let $ …