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Laplace distribution
The Laplace distribution, also called the double exponential distribution, is a continuous probability distribution with a sharp peak and exponential tails, introduced by Pierre-Simon Laplace in 1774.
Laplace operator
The Laplace operator, or Laplacian, is a differential operator summing a function's second partial derivatives, central to physics equations like Laplace's, the wave, and the Schrödinger equation.
Laplace transform
The Laplace transform, also called the Laplace transformation, is an integral transform that converts a function of time into a function of a complex variable.
Laplace–Beltrami operator
The Laplace–Beltrami operator, introduced by Eugenio Beltrami in the 1860s, generalizes the Laplace operator to Riemannian manifolds as the divergence of the gradient, depending only on the metric.
Laplace–Stieltjes transform
The Laplace–Stieltjes transform of a nonnegative random variable X is E(e^{-sX}), defined for s ≥ 0 as the Stieltjes integral of e^{-sx} against the distribution function, applying to distributions with atoms or densities alike.
Laplace's equation
Laplace's equation, also known as Laplace's differential equation, is the second-order partial differential equation Δu = 0, the prototype of elliptic equations; its solutions are harmonic functions describing gravitational and electrostatic potentials.
Laplace's method
Laplace's method is a technique of asymptotic analysis for estimating Laplace integrals with a large parameter, using only the region near the exponent's maximum; it dates to Laplace's 1774 memoir.
Laplacian matrix
The Laplacian matrix, also called the graph Laplacian or Kirchhoff matrix, is a graph matrix L = D − A whose eigenvalues reveal connectivity, spanning trees, and clustering.
Large cardinal
A large cardinal, also called a large cardinal axiom, is an uncountable cardinal so large that its existence is unprovable in ZFC, set theory's standard axioms.
Large cardinal hierarchy
The large cardinal hierarchy orders large-cardinal axioms by consistency strength, usually as a chain of equiconsistencies running from measurable cardinals up to the rank-into-rank axioms, the strongest not known to contradict choice.
Large numbers
Large numbers, or very large numbers, are numbers far beyond everyday counting, conventionally starting around a million, expressed through -illion names, scientific notation, SI prefixes, and googology.
Large sieve
The large sieve is a method in analytic number theory, introduced by Yuri Linnik in 1941, that controls a sequence of numbers simultaneously modulo many small moduli.
Largest known prime number
The largest known prime number, the Mersenne prime 2^136,279,841 − 1, has 41,024,320 digits and was found by Luke Durant via the GIMPS project in 2024.
LaSalle's invariance principle
LaSalle's invariance principle is a theorem in dynamical systems, due to J. P. LaSalle in the 1950s, giving asymptotic stability from a Lyapunov function with nonpositive derivative.
Lasso (statistics)
The lasso, or least absolute shrinkage and selection operator, is a regression method introduced by Robert Tibshirani in 1996 that shrinks some coefficients to exactly zero, giving sparse, interpretable models.
Last observation carried forward
Last observation carried forward (LOCF) is a statistical imputation method that fills missing values in longitudinal data with each subject's last observed value, long common in clinical trials.
Latent change score model
A latent change score (LCS) model is a structural equation model that estimates change over time between latent variables measured on repeated occasions, in univariate or bivariate forms.
Latent class analysis
Latent class analysis, also known as the latent class model, is a statistical method that sorts cases into unobserved subgroups, called latent classes, using categorical variables.
Latent Dirichlet allocation
Latent Dirichlet allocation (LDA) is a generative probabilistic model in which each document is a mixture over latent topics, introduced by Blei, Ng, and Jordan in 2003 and the standard starting point for topic modeling.
Latent factor mixed model
A latent factor mixed model (LFMM) is a regression method that tests genetic loci for association with environmental variables while correcting for population structure through latent factors.
Latent growth curve model
A latent growth curve model is a structural equation modeling method that estimates change over time by treating each person's intercept and slope as latent variables.
Latent growth modeling
Latent growth modeling is a structural equation modeling technique that estimates how people change over time, treating each person's initial status and rate of change as latent variables.
Latent profile analysis
Latent profile analysis (LPA), also called finite mixture modeling, is a statistical method that classifies individuals into unobserved subgroups, called profiles, based on patterns in continuous variables.
Latent space model (network analysis)
A latent space model is a statistical model for network data representing each node as a point in an unobserved latent space, with edge probabilities determined by latent positions.
Latent transition analysis
Latent transition analysis, also known as latent Markov modeling, is a longitudinal statistical method that extends latent class analysis to estimate how individuals move between unobserved subgroups over time.
Latent variable model
A latent variable model is a probabilistic model in which each observed data point is paired with an unobserved variable, explaining high-dimensional data with few degrees of freedom.
Latin hypercube sampling
Latin hypercube sampling (LHS) is a stratified Monte Carlo method, introduced by McKay, Beckman, and Conover in 1979, that stratifies each input dimension to reduce variance in uncertainty analysis.
Latin square
A Latin square, or row-column design, is an n × n array of n symbols, each appearing exactly once in every row and column, named for Euler's Latin letters.
Lattice (group)
A lattice, or point lattice, is a discrete additive subgroup of Euclidean space, a periodic set of points central to the geometry of numbers, sphere packings, and cryptography.
Lattice (order)
A lattice is a partially ordered set in which every pair of elements has a greatest lower bound (meet) and a least upper bound (join).