Matches in SemOpenAlex for { <https://semopenalex.org/work/W4289304893> ?p ?o ?g. }
Showing items 1 to 70 of
70
with 100 items per page.
- W4289304893 abstract "Given a selfadjoint polynomial $P(X,Y)$ in two noncommuting selfadjoint indeterminates, we investigate the asymptotic eigenvalue behavior of the random matrix $P(A_N,B_N)$, where $A_N$ and $B_N$ are independent Hermitian random matrices and the distribution of $B_N$ is invariant under conjugation by unitary operators. We assume that the empirical eigenvalue distributions of $A_N$ and $B_N$ converge almost surely to deterministic probability measures $mu $ and $nu$, respectively. In addition, the eigenvalues of $A_N$ and $B_N$ are assumed to converge uniformly almost surely to the support of $mu$ and $nu,$ respectively, except for a fixed finite number of fixed eigenvalues (spikes) of $A_N$. It is known that almost surely the empirical distribution of the eigenvalues of $P(A_N,B_N)$ converges to a certain deterministic probability measure $eta$ (sometimes denoted $eta=P^square(mu,nu)$) and, when there are no spikes, the eigenvalues of $P(A_N,B_N)$ converge uniformly almost surely to the support of $eta$. When spikes are present, we show that the eigenvalues of $P(A_N,B_N)$ still converge uniformly to the support of $eta$, with the possible exception of certain isolated outliers whose location can be determined in terms of $mu,nu,P$, and the spikes of $A_N$. We establish a similar result when $B_N$ is replaced by a Wigner matrix. The relation between outliers and spikes is described using the operator-valued subordination functions of free probability theory. These results extend known facts from the special case in which $P(X,Y)=X+Y$." @default.
- W4289304893 created "2022-08-02" @default.
- W4289304893 creator A5071984503 @default.
- W4289304893 creator A5085038106 @default.
- W4289304893 creator A5008278856 @default.
- W4289304893 date "2018-11-05" @default.
- W4289304893 modified "2023-09-24" @default.
- W4289304893 title "On the outlying eigenvalues of a polynomial in large independent random matrices" @default.
- W4289304893 hasPublicationYear "2018" @default.
- W4289304893 type Work @default.
- W4289304893 citedByCount "0" @default.
- W4289304893 crossrefType "posted-content" @default.
- W4289304893 hasAuthorship W4289304893A5008278856 @default.
- W4289304893 hasAuthorship W4289304893A5071984503 @default.
- W4289304893 hasAuthorship W4289304893A5085038106 @default.
- W4289304893 hasBestOaLocation W42893048931 @default.
- W4289304893 hasConcept C110121322 @default.
- W4289304893 hasConcept C114614502 @default.
- W4289304893 hasConcept C118615104 @default.
- W4289304893 hasConcept C121332964 @default.
- W4289304893 hasConcept C134306372 @default.
- W4289304893 hasConcept C158693339 @default.
- W4289304893 hasConcept C17744445 @default.
- W4289304893 hasConcept C199539241 @default.
- W4289304893 hasConcept C202444582 @default.
- W4289304893 hasConcept C21031990 @default.
- W4289304893 hasConcept C33923547 @default.
- W4289304893 hasConcept C62520636 @default.
- W4289304893 hasConcept C64812099 @default.
- W4289304893 hasConcept C67820243 @default.
- W4289304893 hasConcept C90119067 @default.
- W4289304893 hasConcept C94940 @default.
- W4289304893 hasConcept C96214315 @default.
- W4289304893 hasConceptScore W4289304893C110121322 @default.
- W4289304893 hasConceptScore W4289304893C114614502 @default.
- W4289304893 hasConceptScore W4289304893C118615104 @default.
- W4289304893 hasConceptScore W4289304893C121332964 @default.
- W4289304893 hasConceptScore W4289304893C134306372 @default.
- W4289304893 hasConceptScore W4289304893C158693339 @default.
- W4289304893 hasConceptScore W4289304893C17744445 @default.
- W4289304893 hasConceptScore W4289304893C199539241 @default.
- W4289304893 hasConceptScore W4289304893C202444582 @default.
- W4289304893 hasConceptScore W4289304893C21031990 @default.
- W4289304893 hasConceptScore W4289304893C33923547 @default.
- W4289304893 hasConceptScore W4289304893C62520636 @default.
- W4289304893 hasConceptScore W4289304893C64812099 @default.
- W4289304893 hasConceptScore W4289304893C67820243 @default.
- W4289304893 hasConceptScore W4289304893C90119067 @default.
- W4289304893 hasConceptScore W4289304893C94940 @default.
- W4289304893 hasConceptScore W4289304893C96214315 @default.
- W4289304893 hasLocation W42893048931 @default.
- W4289304893 hasLocation W42893048932 @default.
- W4289304893 hasLocation W42893048933 @default.
- W4289304893 hasLocation W42893048934 @default.
- W4289304893 hasLocation W42893048935 @default.
- W4289304893 hasOpenAccess W4289304893 @default.
- W4289304893 hasPrimaryLocation W42893048931 @default.
- W4289304893 hasRelatedWork W1604331816 @default.
- W4289304893 hasRelatedWork W1989304900 @default.
- W4289304893 hasRelatedWork W2146910515 @default.
- W4289304893 hasRelatedWork W2588381893 @default.
- W4289304893 hasRelatedWork W2895437888 @default.
- W4289304893 hasRelatedWork W2963311229 @default.
- W4289304893 hasRelatedWork W2964124558 @default.
- W4289304893 hasRelatedWork W3100847938 @default.
- W4289304893 hasRelatedWork W4289304893 @default.
- W4289304893 hasRelatedWork W4297074431 @default.
- W4289304893 isParatext "false" @default.
- W4289304893 isRetracted "false" @default.
- W4289304893 workType "article" @default.