Related papers: Non-Markov quantum belief propagation
We resolve the long-standing problem of elucidating the cutoff phenomenon for a vast and important class of Markov processes, namely Markov diffusions with non-negative Bakry-\'Emery curvature. More precisely, we prove that any sequence of…
We investigate dynamics of an inference algorithm termed the belief propagation (BP) when employed in spin glass (SG) models and show that its macroscopic behaviors can be traced by recursive updates of certain auxiliary field distributions…
In this paper we study the semi-global (approximate) state feedback stabilization of an infinite dimensional quantum stochastic system towards a target state. A discrete-time Markov chain on an infinite-dimensional Hilbert space is used to…
In this Letter we study the effects of the Modified Uncertainty Principle as proposed in Ali et al. (2009) [5] in simple quantum mechanical systems and study its thermodynamic properties. We have assumed that the quantum particles follow…
Bayesian nonparametric statistics is an area of considerable research interest. While recently there has been an extensive concentration in developing Bayesian nonparametric procedures for model checking, the use of the Dirichlet process,…
Safety is an essential requirement for reinforcement learning systems. The newly emerging framework of robust constrained Markov decision processes allows learning policies that satisfy long-term constraints while providing guarantees under…
Transition path theory (TPT) for diffusion processes is a framework for analysing the transitions of multiscale ergodic diffusion processes between disjoint metastable subsets of state space. Most methods for applying TPT involve the…
The quantum fluctuation-dissipation theorem is a central ingredient in the construction of quantum dynamics of Brownian motion which necessarily is non-Markovian. Yet, often Markovian approximations to quantum dynamics are studied in the…
We give computable bounds on the rate of convergence of the transition probabilities to the stationary distribution for a certain class of geometrically ergodic Markov chains. Our results are different from earlier estimates of Meyn and…
The canonical problem of solving a system of linear equations arises in numerous contexts in information theory, communication theory, and related fields. In this contribution, we develop a solution based upon Gaussian belief propagation…
We define two algorithms for propagating information in classification problems with pairwise relationships. The algorithms are based on contraction maps and are related to non-linear diffusion and random walks on graphs. The approach is…
Message passing algorithms have proved surprisingly successful in solving hard constraint satisfaction problems on sparse random graphs. In such applications, variables are fixed sequentially to satisfy the constraints. Message passing is…
What is the minimum time required to take a temperature? In this paper, we solve this question for a large class of processes where temperature is inferred by measuring a probe (the thermometer) weakly coupled to the sample of interest, so…
An approximate partition functional is derived for the infinite-dimensional Hubbard model. This functional naturally includes the exact solution of the Falicov-Kimball model as a special case, and is exact in the uncorrelated and atomic…
In the quest for scalable Bayesian computational algorithms we need to exploit the full potential of existing methodologies. In this note we point out that message passing algorithms, which are very well developed for inference in graphical…
The canonical problem of solving a system of linear equations arises in numerous contexts in information theory, communication theory, and related fields. In this contribution, we develop a solution based upon Gaussian belief propagation…
We provide a coupling proof of Doob's theorem which says that the transition probabilities of a regular Markov process which has an invariant probability measure $\mu$ converge to $\mu$ in the total variation distance. In addition we show…
Dynamical random walk of classical particle in thermodynamically equilibrium fluctuating medium, - Gaussian random potential field, - is considered in the framework of explicit stochastic representation of deterministic interactions. We…
The applicability conditions of a recently reported Central Limit Theorem-based approximation method in statistical physics are investigated and rigorously determined. The failure of this method at low and intermediate temperature is proved…
We study the performance of different message passing algorithms in the two dimensional Edwards Anderson model. We show that the standard Belief Propagation (BP) algorithm converges only at high temperature to a paramagnetic solution. Then,…