A Retrospective and Prospective Survey of the Monte Carlo Method
Data up to Jan 2025
Total Citations Per Year
Abstract
References (158)
Equation of State Calculations by Fast Computing Machines
1953 • 34,935 citations
The Monte Carlo Method
1949 • 5,519 citations
Matrix Iterative Analysis
1963 • 4,155 citations
�ber die partiellen Differenzengleichungen der mathematischen Physik
1928 • 3,608 citations
A Note on the Generation of Random Normal Deviates
1958 • 3,337 citations
Studies in Molecular Dynamics. I. General Method
1959 • 2,318 citations
The algebraic eigenvalue problem
1966 • 2,137 citations
On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals
1960 • 1,843 citations
An Introduction to the Theory of Numbers.
1961 • 1,826 citations
Functional analysis in normed spaces
1952 • 1,606 citations
A Survey of Matrix Theory and Matrix Inequalities
1965 • 1,493 citations
Rounding errors in algebraic processes
1964 • 1,377 citations
�ber die Gleichverteilung von Zahlen mod. Eins
1916 • 1,195 citations
THE THEORY OF MATRICES IN NUMERICAL ANALYSIS
1965 • 1,179 citations
Functional Analysis: Theory and Applications
1965 • 1,129 citations
Monte Carlo Calculation of the Average Extension of Molecular Chains
1955 • 1,047 citations
�ber die analytischen Methoden in der Wahrscheinlichkeitsrechnung
1931 • 1,007 citations
The shortest path through many points
1959 • 933 citations
Computer Solution of Linear Algebraic Systems
1970 • 845 citations
Studies in Molecular Dynamics. II. Behavior of a Small Number of Elastic Spheres
1960 • 796 citations
Methods in computational physics
1973 • 646 citations
MONTE CARLO METHODS FOR SOLVING MULTIVARIABLE PROBLEMS
1960 • 508 citations
On irregularities of distribution
1954 • 491 citations
Theorie des Fonctions Numeriques Simplement Periodiques
1878 • 461 citations
Monte Carlo Principles and Neutron Transport Problems
1971 • 459 citations
Monte Carlo Calculations on Intranuclear Cascades. I. Low-Energy Studies
1958 • 431 citations
Introduction to Mathematical Probability.
1938 • 406 citations
A Retrospective and Prospective Survey of the Monte Carlo Method
1970 • 346 citations
Random Number Generators
1962 • 337 citations
On the Numerical Factors of the Arithmetic Forms α n ± β n
1913 • 328 citations
Monte Carlo Calculations on Intranuclear Cascades. II. High-Energy Studies and Pion Processes
1958 • 319 citations
Monte Carlo Calculations of the Ground State of Three- and Four-Body Nuclei
1962 • 299 citations
Fourier Analysis of Uniform Random Number Generators
1967 • 295 citations
Some Continuous Monte Carlo Methods for the Dirichlet Problem
1956 • 284 citations
An Introduction to Linear Algebra.
1956 • 277 citations
A new Monte Carlo technique: antithetic variates
1956 • 258 citations
Uniform Random Number Generators
1965 • 247 citations
Good lattice points, discrepancy, and numerical integration
1966 • 242 citations
Funktionen von beschränkter Variatiou in der Theorie der Gleichverteilung
1961 • 234 citations
Functional Analysis
1965 • 232 citations
Further Results on Monte Carlo Equations of State
1954 • 229 citations
Bemerkungen zur Theorie der Diophantischen Approximationen
1922 • 200 citations
A method for numerical integration
1961 • 200 citations
Randomness and Random Sampling Numbers
1938 • 192 citations
Equation of State of Classical Hard Spheres at High Density
1962 • 175 citations
Zur angen�herten Berechnung mehrfacher Integrale
1962 • 163 citations
PROBABLE ERROR OF A CORRELATION COEFFICIENT
1908 • 161 citations
A fast procedure for generating normal random variables
1964 • 158 citations
Sequential Monte Carlo
1962 • 157 citations
Studies in Molecular Dynamics. III. A Mixture of Hard Spheres
1964 • 157 citations
Application of the Monte Carlo Method to the Lattice-Gas Model. I. Two-Dimensional Triangular Lattice
1959 • 153 citations
THE PROPERTIES OF A STOCHASTIC MODEL FOR TWO COMPETING SPECIES
1958 • 145 citations
Monte Carlo Calculations. II. The Reactions of Alkali Atoms with Methyl Iodide
1962 • 137 citations
The Monte Carlo method in quantum statistical mechanics
1962 • 132 citations
Some applications of multidimensional integration by parts
1968 • 131 citations
On successive settings of an arc on the circumference of a circle
1958 • 127 citations
Note on irregularities of distribution
1956 • 125 citations
An Introduction to the Theory of Linear Spaces.
1962 • 123 citations
Symposium on Monte Carlo Methods.
1957 • 119 citations
A New Pseudo-Random Number Generator
1960 • 109 citations
Fibonacci Series Modulo m
1960 • 108 citations
A Million Random Digits with 100,000 Normal Deviates.
1955 • 107 citations
Matrix Inversion by a Monte Carlo Method
1950 • 105 citations
Calculation of Order Parameters in a Binary Alloy by the Monte Carlo Method
1959 • 101 citations
A Comparison of Methods for Generating Normal Deviates on Digital Computers
1959 • 98 citations
The Mathematical Basis of Monte Carlo and Quasi-Monte Carlo Methods
1968 • 95 citations
Deterministic simulation of random processes
1963 • 91 citations
A Monte Carlo method applied to the Heisenberg ferromagnet
1964 • 88 citations
Monte Carlo Calculation of the Order-Disorder Transformation in the Body-Centered Cubic Lattice
1961 • 88 citations
Reflection and transmission of gamma radiation by barriers: Semianalytic Monte-Carlo calculation
1956 • 88 citations
The extreme and L2 discrepancies of some plane sets
1969 • 84 citations
Lectures on linear algebra
1961 • 83 citations
Serial Correlation in the Generation of Pseudo-Random Numbers
1960 • 81 citations
“Monte Carlo” Methods for the Iteration of Linear Operators
1953 • 81 citations
Monte Carlo Procedure for Statistical Mechanical Calculations in a Grand Canonical Ensemble of Lattice Systems
1963 • 81 citations
Foundations of General Topology.
1964 • 79 citations
Generating discrete random variables in a computer
1963 • 76 citations
Tables of random sampling numbers
1946 • 74 citations
Stochastic wave function for atomic helium
1966 • 69 citations
An a priori determination of serial correlation in computer generated random numbers
1961 • 69 citations
Thermodynamic properties of mixtures of hard sphere molecules by Monte Carlo methods
1963 • 67 citations
Expressing a Random Variable in Terms of Uniform Random Variables
1961 • 64 citations
Diophantische Ungleichungen. I. Zur Gleichverteilung Modulo Eins
1931 • 62 citations
A sampling method for determining the lowest eigenvalue and the principal eigenfunction of Schrodingers equation
1950 • 61 citations
The Monte Carlo Method: The Method of Statistical Trials.
1967 • 61 citations
General principles of antithetic variates
1956 • 60 citations
Order-Disorder Events Produced by Single Vacancy Migration
1963 • 60 citations
Weighted Uniform Sampling — a Monte Carlo Technique for Reducing Variance
1966 • 58 citations
Computation of Order Parameters in an Ising Lattice by the Monte Carlo Method
1960 • 57 citations
On Monte Carlo Methods in Congestion Problems: I. Searching for an Optimum in Discrete Situations
1965 • 56 citations
Mixed Congruential Random Number Generators for Decimal Machines
1963 • 54 citations
The Monte Carlo Method
1958 • 52 citations
Monte Carlo Calculations for the Two-Dimensional Triangular Lattice Gas: Supercritical Region
1963 • 52 citations
Notes on a New Pseudo-Random Number Generator
1961 • 51 citations
On the theory of diophantine approximations. I1 (on a problem of A. Ostrowski)
1957 • 51 citations
Method of Statistical Testing. Monte Carlo Method
1965 • 50 citations
A Note on the Inversion of Matrices by Random Walks
1952 • 45 citations
Negative probability
1945 • 44 citations
Reflection and transmission of gamma radiation by barriers: Monte-Carlo calculation by a collision-density method
1955 • 43 citations
Importance Sampling in Monte Carlo Shielding Calculations: I. Neutron Penetration through Thick Hydrogen Slabs
1963 • 41 citations
Generating Exponential Random Variables
1961 • 41 citations
Numerical Estimation of the Partition Function in Quantum Statistics
1962 • 40 citations
On the theory of random search
1965 • 40 citations
A Method for Increasing the Efficiency of Monte Carlo Integration
1957 • 39 citations
Random number generator
1956 • 38 citations
Conditional Monte Carlo
1956 • 34 citations
The distribution of the sequence {nξ}(n = 0, 1, 2, …)
1965 • 33 citations
XVI. On james Bernouilli's theorem in probabilities
1899 • 32 citations
Method in randomness
1965 • 32 citations
Mixed Congruential Random Number Generators for Binary Machines
1964 • 32 citations
Continued fraction expansions of algebraic numbers
1962 • 31 citations
An Extension of the Buffon Needle Problem
1953 • 26 citations
Statistical Treatment of Values of First 2,000 Decimal Digits of e and of /pi Calculated on the ENIAC
1950 • 26 citations
A Property of Randomness of an Arithmetical Function
1953 • 26 citations
Calculation of cyclization probabilities and other configuration properties of alkane-type chains by a Monte Carlo method
1963 • 25 citations
Random walks and the eigenvalues of elliptic difference equations
1951 • 25 citations
A Uniform Random Number Generator Based on the Combination of Two Congruential Generators
1967 • 24 citations
On the mean duration of random walks
1951 • 24 citations
Proof of the antithetic variates theorem for n > 2
1958 • 23 citations
A monte-carlo method for solving a class of integral equations
1951 • 22 citations
On a sequence of points of interest for numerical quadrature
1966 • 22 citations
On the Numerical Factors of the Arithmetic Forms α n ± β n
1913 • 22 citations
Some New Results in Pseudo-Random Number Generation
1967 • 21 citations
On Sequences of Pseudo-Random Numbers of Maximal Length
1958 • 20 citations
Random Sampling from the Normal Distribution
1961 • 19 citations
The Monte Carlo solution of some integral equations
1954 • 19 citations
Good lattice points in the sense of Hlawka and Monte-Carlo integration
1968 • 18 citations
The application of Monte Carlo methods to physicochemical problems
1962 • 18 citations
The Monte Carlo Method in Quantum Statistics
1968 • 18 citations
Ernie--A Mathematical and Statistical Analysis
1959 • 17 citations
Groups and Conditional Monte Carlo
1957 • 17 citations
The behavior of pseudo-random sequences generated on computers by the multiplicative congruential method
1962 • 17 citations
Autocorrelations between pseudo-random numbers
1964 • 16 citations
On the Duration of Random Walks
1951 • 16 citations
On the relative merits of correlated and importance sampling for Monte Carlo integration
1965 • 16 citations
Remarks on a Monte Carlo integration method
1964 • 15 citations
On the estimation of an eigenvalue by an additive functional of a stochastic process, with special reference to the Kac-Donsker method
1952 • 14 citations
On uniform distribution of algebraic numbers
1953 • 14 citations
A Generalisation of the Antithetic Variate Technique for Evaluating Integrals
1957 • 14 citations
Error Rates in Differentially Coherent Phase Systems in Non-Gaussian Noise
1966 • 14 citations
Pseudo-Random Elements for Computers
1959 • 13 citations
On the discrepancy of certain sequences mod. 1
1963 • 13 citations
Coupon Collector's Test for Random Digits
1955 • 12 citations
The Monte Carlo Method as a Natural Mode of Expression in Operations Research
1953 • 12 citations
On exponential and other random variable generators
1961 • 12 citations
High Speed Sampling
1951 • 10 citations
Diophantische Approximationen
2023 • 10 citations
A Practical Demonstration of a Needle Experiment Designed to give a Number of Concurrent Estimates of &#960
1961 • 10 citations
A Unified Approach to Monte Carlo methods and an Application to a Multigroup Calculation of Absorption Rates
1962 • 9 citations
A Monte Carlo Analysis of the Ground Controlled Approach System
1957 • 9 citations
An interpretation of negative probabilities
1966 • 8 citations
Some theorems concerning pseudo-random numbers
1965 • 8 citations
Study of Tumor Cell Populations by Monte Carlo Methods
1955 • 7 citations
A rigorous lower bound for the efficiency of a Monte Carlo technique
1964 • 4 citations
A Simple Principle of Unification in the Elementary Theory of Numbers
1929 • 4 citations
Monte Carlo Matrix Inversion and Recurrent Events
1953 • 4 citations
On Discrete Operators Connected with the Dirichlet Problem
1956 • 3 citations
Monte Carlo Matrix Calculation with Punched Card Machines
1951 • 3 citations