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Related papers: Poisson convergence on the free Poisson algebra

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In this paper, an alternative mixed Poisson distribution is proposed by amalgamating Poisson distribution and a modification of the Quasi Lindley distribution. Some fundamental structural properties of the new distribution, namely the shape…

Methodology · Statistics 2021-10-26 Ramajeyam Tharshan , Pushpakanthie Wijekoon

The counterintuitive fact that wave chaos appears in the bending spectrum of free rectangular thin plates is presented. After extensive numerical simulations, varying the ratio between the length of its sides, it is shown that (i) frequency…

The fully coupled dynamic interaction problem of the free surface of an incompressible fluid and a rigid body beneath it, in an inviscid, irrotational framework and in the absence of surface tension, is considered. Evolution equations of…

Fluid Dynamics · Physics 2024-08-26 Banavara N. Shashikanth

We compute the exact rates of convergence in total variation associated with the 'fourth moment theorem' by Nualart and Peccati (2005), stating that a sequence of random variables living in a fixed Wiener chaos verifies a central limit…

Probability · Mathematics 2013-05-08 Ivan Nourdin , Giovanni Peccati

Periodicity plays a significant role in the chaos theory from the beginning since the skeleton of chaos can consist of infinitely many unstable periodic motions. This is true for chaos in the sense of Devaney [1], Li-Yorke [2] and the one…

Chaotic Dynamics · Physics 2017-04-25 Marat Akhmet , Mehmet Onur Fen

For a class of random matrix ensembles with correlated matrix elements, it is shown that the density of states is given by the Wigner semi-circle law. This is applied to effective Hamiltonians related to the Anderson model in dimensions…

Mathematical Physics · Physics 2007-05-23 Jeffrey H. Schenker , Hermann Schulz-Baldes

There is an explicit resolution of the Poisson reduction of four planar point vortices, in the case that three of the vortex strengths are equal and the total vorticity is zero. The resolution, a Hamiltonian system on a unified symplectic…

Mathematical Physics · Physics 2023-11-02 George W. Patrick

The statistics of gaps between quantum energy levels is a hallmark criterion in quantum chaos and quantum integrability studies. The relevant distributions corresponding to exactly integrable vs. fully chaotic systems are universal and…

Statistical Mechanics · Physics 2026-04-27 Ben Craps , Marine De Clerck , Oleg Evnin , Maxim Pavlov

The central limit theorem, the invariance principle and the Poisson limit theorem for the hierarchy of freeness are studied. We show that for given natural m the limit laws can be expressed in terms of non-crossing partitions of depth…

Quantum Algebra · Mathematics 2014-07-25 Uwe Franz , Romuald Lenczewski

We analyse the problem of defining a Poisson bracket structure on the space of solutions of the equations of motions of first order Hamiltonian field theories. The cases of Hamiltonian mechanical point systems (as a (0 + 1)-dimensional…

Mathematical Physics · Physics 2024-12-24 Florio M. Ciaglia , Fabio Di Cosmo , Alberto Ibort , Giuseppe Marmo , Luca Schiavone , Alessandro Zampini

We study the poor-biased model for money exchange introduced in [2]: agents are being randomly picked at a rate proportional to their current wealth, and then the selected agent gives a dollar to another agent picked uniformly at random.…

Probability · Mathematics 2025-01-15 Roberto Cortez , Fei Cao

We establish a general inequality on the Poisson space, yielding an upper bound for the distance in total variation between the law of a regular random variable with values in the integers and a Poisson distribution. Several applications…

Probability · Mathematics 2012-04-18 Giovanni Peccati

By exploiting the well-known observation that size-biasing or zero-biasing an infinitely divisible random variable may be achieved by adding an independent increment, combined with tools from Stein's method for compound Poisson and Gaussian…

Probability · Mathematics 2025-12-11 Fraser Daly

Under mild conditions on a family of independent random variables $(X_n)$ we prove that almost sure convergence of a sequence of tetrahedral polynomial chaoses of uniformly bounded degrees in the variables $(X_n)$ implies the almost sure…

Probability · Mathematics 2019-10-24 Radosław Adamczak

The Poisson structure is constructed for a model in which spatial coordinates of configuration space are noncommutative and satisfy the commutation relations of a Lie algebra. The case is specialized to that of the group SU(2), for which…

High Energy Physics - Theory · Physics 2015-05-13 Mohammad Khorrami , Amir H. Fatollahi , Ahmad Shariati

In quantum theory, the no-information-without-disturbance and no-free-information theorems express that those observables that do not disturb the measurement of another observable and those that can be measured jointly with any other…

Quantum Physics · Physics 2019-07-10 Teiko Heinosaari , Leevi Leppäjärvi , Martin Plávala

We characterize semicircular distribution by the freeness of linear and quadratic forms in noncommutative random variables from a tracial $W^*$-probability space with relaxed moment conditions.

Operator Algebras · Mathematics 2012-12-06 G. P. Chistyakov , F. Götze , F. Lehner

Wigner integrals and the corresponding Wigner chaos were introduced by P. Biane and R. Speicher in 1998 as a non-commutative counterpart of classical Wiener-It\^o integrals and the corresponding Wiener-It\^o chaos, respectively, in free…

Operator Algebras · Mathematics 2016-03-08 Tobias Mai

We investigate random graphs on the points of a Poisson process in $d$-dimensional space, which combine scale-free degree distributions and long-range effects. Every Poisson point carries an independent random mark and given marks and…

Probability · Mathematics 2022-05-02 Peter Gracar , Markus Heydenreich , Christian Mönch , Peter Mörters

We establish necessary and sufficient conditions implying that the product of $m\geq 2$ Poisson functionals, living in a finite sum of Wiener chaoses, is square-integrable. Our conditions are expressed in terms of iterated add-one cost…

Probability · Mathematics 2025-06-02 Lorenzo Cristofaro , Giovanni Peccati