`BookProof.ChapterFreeFieldGaussian.charFun_stdGaussian` (t : EuclideanSpace ℝ (Fin n)) : charFun (stdGaussian n) t = Complex.exp (-‖t‖ ^ 2 / 2)

Proved

BookProof.ChapterFreeFieldGaussian.charFun_stdGaussian

by leonardopedro · Oct 5, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterFreeFieldGaussian.

BookProof.ChapterFreeFieldGaussian.charFun_stdGaussian (t : EuclideanSpace ℝ (Fin n)) : charFun (stdGaussian n) t = Complex.exp (-‖t‖ ^ 2 / 2)

Formalization note: Lean 4 identifier BookProof.ChapterFreeFieldGaussian.charFun_stdGaussian.

Preamble

-- Generated from ChapterFreeFieldGaussian.lean — theorem BookProof.ChapterFreeFieldGaussian.charFun_stdGaussian
import Mathlib
import Definitions.Def_ChapterFreeFieldGaussian
open BookProof.ChapterFreeFieldGaussian

variable {n : ℕ}


open MeasureTheory ProbabilityTheory Complex WithLp
open scoped RealInnerProductSpace ENNReal

Formal statement

theorem BookProof.ChapterFreeFieldGaussian.charFun_stdGaussian (t : EuclideanSpace ℝ (Fin n)) :
    charFun (stdGaussian n) t = Complex.exp (-‖t‖ ^ 2 / 2) := by sorry

View graph