Continuous distribution with density (2πσ²)^(-1/2) exp(-(x-μ)²/2σ²). Attractor of the CLT and maximum-entropy distribution for fixed mean and variance.
Gaussian (normal) distribution
Related concepts
- Central limit theorem
- Binomial theorem
- Real numbers (ℝ)
- Lp space
- Brownian motion (Wiener process)
- Wigner-Dyson level-spacing statistics P_beta(s) for chaotic spectra
- Maxwell-Boltzmann distribution
- Single-molecule biophysics
- Fluorescence correlation spectroscopy (FCS)
- Langevin equation (biophysical use)
- Glauber coherent state
- Multimessenger astronomy
- Mahalanobis d² = (x−μ)ᵀΣ⁻¹(x−μ): covariance-respecting distance metric
- Debye-Waller framework: I(q)/I_0 = exp(−⟨u²⟩·q²) (thermal-displacement Gaussian-in-q² attenuation)
- Generalization gradient: p_gauss(d) = exp(−d²/2σ²); p_shep(d) = exp(−d/σ); metric-space-dependent
- Jukes-Cantor 69 molecular distance: d=−3/4·log(1−4p/3); Zuckerkandl-Pauling extension
- Genome-wide association study (GWAS)