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Suzuki-Trotter decomposition is a well-known technique used to calculate the partition function of quantum spin systems, in which the imaginary-time dependence of the partition function occurs inevitably. Since it is very difficult to…
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The master equation and, more generally, Markov processes are routinely used as models for stochastic processes. They are often justified on the basis of randomization and coarse-graining assumptions. Here instead, we derive n-th order…
Historically time-reversibility of the transitions or processes underpinning Markov chain Monte Carlo methods (MCMC) has played a key r\^ole in their development, while the self-adjointness of associated operators together with the use of…
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How stochastic, microscopic events generate deterministic, macroscopic properties is a fundamental question in physics. We address this question by developing a quantum master equation model for concentrated radical solutions, where random…
Colloids have a striking relevance in a wide spectrum of industrial formulations, spanning from personal care products to protective paints. Their behaviour can be easily influenced by extremely weak forces, which disturb their…
We introduce jump processes in R^k, called density-profile process, to model biological signaling networks. They describe the macroscopic evolution of finite-size spin-flip models with k types of spins interacting through a non-reversible…
The goal of this paper is to study convergence and error estimates of the Monte Carlo method for the Navier-Stokes equations with random data. To discretize in space and time, the Monte Carlo method is combined with a suitable deterministic…
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We propose a new Monte Carlo method for efficiently sampling trajectories with fixed initial and final conditions in a system with discrete degrees of freedom. The method can be applied to any stochastic process with local interactions,…