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Showing 1 to 14 of 14 for “"free probability"”.
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Second-order finite free probability
Finite free probability is a new field lying at the intersection of random matrix theory and non-commutative probability. It is called “finite” because unlike traditional free probability, which takes the perspective of operators on infinite-dimensional vector spaces, finite free probability …
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Weighted and Self-normalized Sums in Free Probability Theory
… behavior of weighted and self-normalized sums in free probability theory and determine the corresponding rates of convergence to their limit distribution.
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The North Pole Problem and Recent Developments in Infinitesimal Free Probability
… of the combinatorial theory of infinitesimal free probability, one of the principal extensions of free probability theory. We place particular focus on the recently developed theory of real infinitesimal free probability by Cébron and Mingo. We also briefly discuss (complex) infinitesimal free …
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Non-Commutative Probability for the Spectral Analysis of Simplicial Complexes
Free probability theory, invented by Voiculescu, and greatly expanded by Speicher, is a young and active area of research with numerous applications in pure and applied mathematics. This Master thesis is a comprehensive study of a specific result in the recent preprint by C. Vargas, in which Vargas …
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Two-parameter noncommutative Gaussian processes
… random graphs. The modern mathematical theory of free probability is increasingly giving rise to analysis tools specifically adapted to such large-dimensional regimes and, more generally, non-commutative probability is emerging as an area of interdisciplinary interest. This thesis develops a new …
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A graphical calculus for shifted symmetric functions
… This turns out to be given in the language of free probability, in particular, the transition and co-transition measures of Kerov [Ker93, Ker00].
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A graphical calculus for shifted symmetric functions
… This turns out to be given in the language of free probability, in particular, the transition and co-transition measures of Kerov [Ker93, Ker00].
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Kadison -Singer algebras with applications to von Neumann algebras
… of projections. In chapter 4, I use ideas from free probability theory to construct Kadison-Singer algebras with core the free group factors L(Fr) for r < 2. I then introduce two constructions that yield new Kadison-Singer algebras - The maximal join and the minimal join. In chapter 5, I analyse …
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Free products of operator spaces and free Markov processes
<p>Certain (reduced) free product is introduced in the framework of operator spaces. Under the construction, the free product of preduals of von Neumann algebras agrees with the predual of the free product of von Neumann algebras. This answers a question asked by Effros affirmatively. An example is …
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Eigenvalues and low energy eigenvectors of quantum many-body systems
… Schrbdinger operator in one dimension from free probability theory in context of the Anderson model. The second part is devoted to ground states and gap of QMBS. I first give the necessary background on frustration free Hamiltonians, real and imaginary time evolution of quantum spin systems …
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Applied stochastic eigen-analysis
… a framework for computational (non-commutative) “free probability” theory. The class of “algebraic” random matrices is defined and the generators of this class are specified. Algebraicity of a random matrix sequence is shown to act as a certificate of the computability of the limiting eigenvalue …
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Noncommutative rational functions and their finite-dimensional representations
Noncommutative rational functions form a free skew field, a universal object in the category of skew fields. They emerge in various branches of pure and applied mathematics, such as noncom-mutative algebra, automata theory, control theory, free analysis, free real algebraic geometry and free …
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Aspects of Eigenstate Thermalization
… the centrality of random matrix theory and free probability to the ETH. This thesis focuses primarily on a version of the ETH known as ergodic bipartition (EB). The fundamental physical result of the EB is that the entanglement entropy of a subsystem is its thermodynamic entropy, or, more …
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Studies of and methods for electronic properties of large chemical systems
… using the tools of random matrix theory. We use free probability to approximately compute the density of states of a Hamiltonian matrix ensemble without exact diagonalization. We develop an error analysis for this method, and show that it is accurate to the eighth moment of the density of states. …