Professor Ryszard Zieliński's contribution to Monte Carlo methods and random number generators. Uniform asymptotics in statistics

2012 ◽  
Vol 40 (2) ◽  
Author(s):  
Wojciech Niemiro
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Methods ◽  
Random Number ◽  
Uniform Asymptotics ◽  
Random Number Generators

scholarly journals Advanced Statistical Testing of Quantum Random Number Generators

Entropy ◽  
2018 ◽  
Vol 20 (11) ◽  
pp. 886 ◽  
Author(s):  
Aldo Martínez ◽  
Aldo Solis ◽  
Rafael Díaz Hernández Rojas ◽  
Alfred U'Ren ◽  
Jorge Hirsch ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Methods ◽  
Random Number ◽  
Quantum States ◽  
Statistical Testing ◽  
Random Numbers ◽  
Simple Method ◽  
Random Number Generators ◽  
Random Sequences ◽  
Natural Laws

Pseudo-random number generators are widely used in many branches of science, mainly in applications related to Monte Carlo methods, although they are deterministic in design and, therefore, unsuitable for tackling fundamental problems in security and cryptography. The natural laws of the microscopic realm provide a fairly simple method to generate non-deterministic sequences of random numbers, based on measurements of quantum states. In practice, however, the experimental devices on which quantum random number generators are based are often unable to pass some tests of randomness. In this review, we briefly discuss two such tests, point out the challenges that we have encountered in experimental implementations and finally present a fairly simple method that successfully generates non-deterministic maximally random sequences.

Improving Random Number Generators in the Monte Carlo simulations via twisting and combining

2008 ◽  
Vol 178 (6) ◽  
pp. 401-408 ◽  
Author(s):  
Lih-Yuan Deng ◽  
Rui Guo ◽  
Dennis K.J. Lin ◽  
Fengshan Bai
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Random Number ◽  
Random Number Generators

scholarly journals TESTS OF RANDOM NUMBER GENERATORS USING ISING MODEL SIMULATIONS

1996 ◽  
Vol 07 (03) ◽  
pp. 295-303 ◽  
Author(s):  
P. D. CODDINGTON
Keyword(s):  
Monte Carlo ◽  
Ising Model ◽  
Monte Carlo Simulations ◽  
High Performance ◽  
Large Scale ◽  
Random Number ◽  
Random Number Generators ◽  
Lattice Monte Carlo ◽  
High Performance Computers

Large-scale Monte Carlo simulations require high-quality random number generators to ensure correct results. The contrapositive of this statement is also true — the quality of random number generators can be tested by using them in large-scale Monte Carlo simulations. We have tested many commonly-used random number generators with high precision Monte Carlo simulations of the 2-d Ising model using the Metropolis, Swendsen-Wang, and Wolff algorithms. This work is being extended to the testing of random number generators for parallel computers. The results of these tests are presented, along with recommendations for random number generators for high-performance computers, particularly for lattice Monte Carlo simulations.

scholarly journals ANALYSIS OF RANDOM NUMBER GENERATORS USING MONTE CARLO SIMULATION

1994 ◽  
Vol 05 (03) ◽  
pp. 547-560 ◽  
Author(s):  
P.D. CODDINGTON
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Ising Model ◽  
High Precision ◽  
Random Number ◽  
Statistical Tests ◽  
Exact Results ◽  
Random Number Generators ◽  
Monte Carlo Algorithms

Monte Carlo simulation is one of the main applications involving the use of random number generators. It is also one of the best methods of testing the randomness properties of such generators, by comparing results of simulations using different generators with each other, or with analytic results. Here we compare the performance of some popular random number generators by high precision Monte Carlo simulation of the 2-d Ising model, for which exact results are known, using the Metropolis, Swendsen-Wang, and Wolff Monte Carlo algorithms. Many widely used generators that perform well in standard statistical tests are shown to fail these Monte Carlo tests.

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