6,052 articles
Rajeev Motwani
Rajeev Motwani was an Indian-born American computer scientist and Stanford professor known for randomized algorithms, the 2001 Gödel Prize, and advising Google's founders, Sergey Brin and Larry Page.
Raking
Raking, also known as raking ratio estimation or iterative proportional fitting, is a survey weighting method that iteratively adjusts weights so each variable's weighted total matches known population totals.
Ramanujan summation
Ramanujan summation is a technique by Srinivasa Ramanujan for assigning finite values to divergent series, famously giving 1 + 2 + 3 + ⋯ the value −1/12.
Ramanujan tau function
The Ramanujan tau function is the sequence of Fourier coefficients of the weight-12 cusp form Δ, introduced by Ramanujan in 1916. It is multiplicative, satisfies striking congruences, and Deligne proved its size bound in 1974.
Ramanujan–Petersson conjecture
The Ramanujan–Petersson conjecture, also called the Ramanujan conjecture, bounds the Fourier coefficients of modular forms; Ramanujan proposed it in 1916 and Deligne proved it for holomorphic forms.
Ramanujan–Sato series
Ramanujan–Sato series are infinite series for 1/π extending the seventeen series Ramanujan announced in 1914, built from a construction associated with Takeshi Sato; the Chudnovsky series used for world-record π computations belongs to the family.
Ramanujan's congruences
Ramanujan's congruences are three divisibility properties of the partition function p(n), discovered by Srinivasa Ramanujan in 1919: p(5n+4), p(7n+5), and p(11n+6) are divisible by 5, 7, and 11.
Ramanujan's lost notebook
Ramanujan's lost notebook is a manuscript of over 600 formulas written without proofs by the Indian mathematician Srinivasa Ramanujan, found by George Andrews in Cambridge in 1976.
Ramanujan's sum
Ramanujan's sum, also called the Ramanujan sum, is an arithmetic function introduced by Srinivasa Ramanujan in 1916 that sums exponentials over integers coprime to q.
Ramification group
A ramification group is a subgroup in a descending filtration of the Galois group of a local field extension, measuring how deeply each automorphism ramifies it.
Ramon van Handel
Ramon van Handel is a probabilist and professor of mathematics at Princeton University, known for work on random matrices and convex geometry and a 2012 Presidential Early Career Award.
Ramsey cardinal
A Ramsey cardinal is a large cardinal whose finite subsets cannot be 2-colored without a homogeneous set of full size, introduced by Erdős and Hajnal in 1962.
Ramsey number
A Ramsey number is the smallest number of vertices forcing a clique or independent set of given sizes in any graph, with R(3,3) = 6.
Ramsey theory
Ramsey theory is a branch of combinatorics studying how large a structure must be before it is forced to contain a well-organized substructure, named for Frank Ramsey, who proved its central theorem in 1930.
Ramsey's theorem
Ramsey's theorem is a combinatorics result proved by Frank Ramsey in 1930: any coloring of a sufficiently large set's subsets has a large homogeneous subset, founding Ramsey theory.
Rand index
The Rand index is a cluster validation measure scoring the similarity of two clusterings as the fraction of point pairs they classify the same way.
Random assignment
Random assignment, or randomized assignment, places study participants into experimental conditions by chance, balancing known and unknown factors between groups; R. A. Fisher first stated the requirement in 1925.
Random attractor
A random attractor is a family of compact sets in a random dynamical system that attracts all bounded sets, introduced by Crauel, Debussche, and Flandoli in 1997.
Random degree
A random degree is an equivalence class of infinite binary sequences compared by relative randomness, most commonly the K-degrees induced by prefix-free Kolmogorov complexity of initial segments.
Random dynamical system
A random dynamical system is a mathematical model of dynamics driven by noise, developed systematically by Ludwig Arnold, that extends invariant measures, attractors, and bifurcation analysis to randomly forced systems.
Random forcing
Random forcing, also called Solovay forcing, is a set-theoretic forcing method, introduced by Robert Solovay in the 1960s, that adjoins a real avoiding all null sets.
Random geometric graph
A random geometric graph is a random graph whose vertices are points scattered in a geometric space, with edges joining pairs within a fixed distance, introduced by Edgar Gilbert in 1961.
Random graph
A random graph, or random network, is a graph whose edges are placed by random rules, a field founded by Paul Erdős and Alfréd Rényi in the late 1950s.
Random graph matching
Random graph matching is the problem of recovering the hidden vertex correspondence between two correlated random graphs, studied for its sharp thresholds and applications like network de-anonymization.
Random graph process
A random graph process is a random sequence of graphs that starts empty and gains one random edge per step, introduced by Erdős and Rényi in 1960.
Random graph process with choice
A random graph process with choice samples several candidate edges at each step and adds one selected by a rule, best studied in the Achlioptas process introduced around 2000.
Random greedy algorithm
The random greedy algorithm is a randomized construction method that builds a maximal matching or independent set by repeatedly choosing at random among non-conflicting objects until none remain.
Random matrix
A random matrix is a matrix whose entries are drawn from a probability distribution; random matrix theory, begun by Wigner in the 1950s, studies their eigenvalue statistics.
Random measure
A random measure is a measure-valued random object in probability theory, assigning a measure to each experimental outcome, with point processes as its key integer-valued special case.
Random oracle model
The random oracle model is a cryptographic proof technique treating a hash function as a perfectly random public function, formulated by Bellare and Rogaway in 1993.