35 citations · 370 across the 50 of their papers we have counts for
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Hidden processes and hidden Markov processes: classical and quantum
Luigi Accardi, El Gheteb Soueidy, Yun Gang Lu +1
This paper consists of parts. The first part only considers classical processes and introduces two different extensions of the notion of hidden Markov process. In the second pa…
The quantum mechanics canonically associated to free probability Part I: Free momentum and associated kinetic energy
Luigi Accardi, Tarek Hamdi, Yun Gang Lu
After a short review of the quantum mechanics canonically associated with a classical real valued random variable with all moments, we begin to study the quantum mechanics canonica…
Quantum Markov Chains: A unification approach
Luigi Accardi, Abdessatar Souissi, El Gheteb Soueidy
In the present paper we study a unified approach for Quantum Markov Chains. A new quantum Markov property that generalizes the old one, is discussed. We introduce Markov states and…
Construction of a new class of quantum Markov fields
Luigi Accardi, Farrukh Mukhamedov, Abdessatar Souissi
In the present paper, we propose a new construction of quantum Markov fields on arbitrary connected, infinite, locally finite graphs. The construction is based on a specific tessel…
-non-linear second quantization
Luigi Accardi, Ameur Dhahri
Recently, we have constructed a non{linear (polynomial) extension of the 1-mode Heisenberg group and the corresponding Fock and Weyl representations. The transition from the 1-mode…
Polynomial extensions of the Weyl -algebra
Luigi Accardi, Ameur Dhahri
We introduce higher order (polynomial) extensions of the unique (up to isomorphisms) non trivial central extension of the Heisenberg algebra. Using the boson representation of the…
A note on noncommutative unique ergodicity and weighted means
Luigi Accardi, Farrukh Mukhamedov
In this paper we study unique ergodicity of -dynamical system $(\ga,T)$, consisting of a unital -algebra $\ga$ and a Markov operator $T:\ga\mapsto\ga$, relative to its fi…