Everything about Monte Carlo algorithm

🧭 Start here: a 6-step reading path

1. Read the overview: Monte Carlo algorithmA 5-minute orientation
2. Skim a recent paper: Single-step Monte Carlo criticality algorithmInfluential work since 2022
3. Pick up a classic book: Ocean observations with EOS/MODISThe most-reprinted book on the subject
4. Read the landmark paper: New Monte Carlo algorithm: Entropic samplingCited 487 times
5. Go sideways: Solovay–Strassen primality testA closely related topic
6. Go sideways: Randomized algorithmA closely related topic

🏆 Landmark papers (most cited)

• New Monte Carlo algorithm: Entropic sampling

  Jooyoung Lee · 1993 · Physical Review Letters · 487 citations

• Generalized Lanczos algorithm for variational quantum Monte Carlo

  Sandro Sorella · 2001 · Physical Review B · 339 citations

• “Worm” algorithm in quantum Monte Carlo simulations

  N.V Prokof'ev, B.V Svistunov, I.S Tupitsyn · 1998 · Physics Letters A · 241 citations

• A generalized guided Monte Carlo algorithm

  Alan M. Horowitz · 1991 · Physics Letters B · 190 citations

• Implementations of the Monte Carlo EM Algorithm

  Richard A Levine, George Casella · 2001 · Journal of Computational and Graphical Statistics · 183 citations

• Fast Monte Carlo algorithm for supercooled soft spheres

  Tomás S. Grigera, Giorgio Parisi · 2001 · Physical Review E · 182 citations

• An Optimal Algorithm for Monte Carlo Estimation

  Paul Dagum, Richard Karp, Michael Luby · 2000 · SIAM Journal on Computing · 181 citations

• An improved Monte Carlo factorization algorithm

  Richard P. Brent · 1980 · BIT · 112 citations

🆕 Influential since 2022

• Single-step Monte Carlo criticality algorithm

  Qingquan Pan, Nan An, Tengfei Zhang · 2022 · Computer Physics Communications · 31 citations

• Parameter tuning of the firefly algorithm by three tuning methods: Standard Monte Carlo, quasi-Monte Carlo and latin hypercube sampling methods

  Geethu Joy, Christian Huyck, Xin-She Yang · 2025 · Journal of Computational Science · 25 citations

• Validation of RayStation Monte Carlo dose calculation algorithm for multiple LINACs

  Luigi Manco, Kevin Vega, Nicola Maffei · 2023 · Physica Medica · 20 citations

• Backpropagating Hybrid Monte Carlo algorithm for fast Lefschetz thimble calculations

  Genki Fujisawa, Jun Nishimura, Katsuta Sakai · 2022 · Journal of High Energy Physics · 16 citations

• A pseudo-marginal sequential Monte Carlo online smoothing algorithm

  Pierre Gloaguen, Sylvain Le Corff, Jimmy Olsson · 2022 · Bernoulli · 14 citations

📚 Books worth reading

• 📕Ocean observations with EOS/MODISHoward R. Gordon · 1995
• Monte Carlo methods for applied scientistsIvan T. Dimov, Sean McKee · 2005
• Monte Carlo and Quasi-Monte Carlo Methods 2010Leszek Plaskota · 2012
• The Monte Carlo Method in the Physical SciencesJames E. Gubernatis · 2003
• 📕International Youth Workshop on Monte Carlo Methods and Parallel Algorithms, Primorsko, Bulgaria, 24-30 September 1989International Youth Workshop on Monte Carlo Methods and Parallel Algorithms (1st 1989 Primorsko, Bulgaria) · 1991
• 📕Metody Monte-Karlo dli͡a︡ raschetov glubokogo proniknovenii͡a︡ izlucheniĭA. V. Starkov · 1990
• 📕The detector response matrices of the burst and transient source experiment (BATSE) on the Compton Gamma Ray Observatory · 1995
• Explorations in Monte Carlo methodsRonald W. Shonkwiler · 2009

Ranked by number of editions on Open Library, a rough measure of how lasting a book is.

🔗 Related topics

• Solovay–Strassen primality test The Solovay–Strassen primality test, developed by Robert M. Solovay and Volker Strassen in 1977, is a probabilistic primality test to determine if a number…
• Randomized algorithm A randomized algorithm is an algorithm that employs a degree of randomness as part of its logic or procedure. The algorithm typically uses uniformly random…
• BPP (complexity) In computational complexity theory, a branch of computer science, bounded-error probabilistic polynomial time (BPP) is the class of decision problems solvable…
• Las Vegas algorithm In computing, a Las Vegas algorithm is a randomized algorithm that always gives correct results; that is, it always produces the correct result or it informs…
• Volker Strassen Volker Strassen (born April 29, 1936) is a German mathematician, a professor emeritus in the department of mathematics and statistics at the University…
• ZPP (complexity) In complexity theory, ZPP (zero-error probabilistic polynomial time) is the complexity class of problems for which a probabilistic Turing machine exists…
• Primality test A primality test is an algorithm for determining whether an input number is prime. Among other fields of mathematics, it is used for cryptography. Unlike…
• RP (complexity) In computational complexity theory, randomized polynomial time (RP) is the complexity class of decision problems for which a probabilistic Turing machine…