scholarly journals Representation of complex probabilities and complex Gibbs sampling

2018 ◽  
Vol 175 ◽  
pp. 07037 ◽  
Author(s):  
Lorenzo Luis Salcedo

Complex weights appear in Physics which are beyond a straightforward importance sampling treatment, as required in Monte Carlo calculations. This is the wellknown sign problem. The complex Langevin approach amounts to effectively construct a positive distribution on the complexified manifold reproducing the expectation values of the observables through their analytical extension. Here we discuss the direct construction of such positive distributions paying attention to their localization on the complexified manifold. Explicit localized representations are obtained for complex probabilities defined on Abelian and non Abelian groups. The viability and performance of a complex version of the heat bath method, based on such representations, is analyzed.

2014 ◽  
Vol 41 (5) ◽  
pp. 055110 ◽  
Author(s):  
Dietrich Roscher ◽  
Jens Braun ◽  
Jiunn-Wei Chen ◽  
Joaquín E Drut

2016 ◽  
Vol 2016 (5) ◽  
Author(s):  
Andrei Alexandru ◽  
Gökçe Basar ◽  
Paulo F. Bedaque ◽  
Gregory W. Ridgway ◽  
Neill C. Warrington

2018 ◽  
Vol 175 ◽  
pp. 01020 ◽  
Author(s):  
Paulo F. Bedaque

We review recent attempts at dealing with the sign problem in Monte Carlo calculations by deforming the region of integration in the path integral from real to complex fields. We discuss the theoretical foundations, the algorithmic issues and present some results for low dimensional field theories in both imaginary and real time.


2021 ◽  
Vol 134 ◽  
pp. 103688
Author(s):  
Ihsan Farouki ◽  
Rashdan Malkawi ◽  
Sayel Marashdeh

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