# Explicit examples of probability distributions for the energy density in two-dimensional conformal field theory

## TL;DR

This paper derives explicit probability distributions for energy density measurements in 1+1 dimensional conformal field theories, revealing a shifted Gamma distribution form for various averaging functions.

## Contribution

It provides closed-form probability distributions for energy density in CFTs, generalizing previous results and including new families of averaging functions.

## Key findings

- Distributions are shifted Gamma types.
- Results apply to multiple averaging functions.
- Distribution forms are explicitly derived.

## Abstract

Measurements of a weighted energy density average taken in the vacuum state of a conformal field theory in $1+1$ dimensions are randomly distributed with vanishing expectation value. The probability distribution is computed in closed form for two infinite families of averaging functions, generalising previously known examples. These examples may be further generalised by restriction to a half-line In all cases the distribution is that of a shifted Gamma distribution.