FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W2962968734> ?p ?o ?g. }

• W2962968734 endingPage "327" @default.
• W2962968734 startingPage "275" @default.
• W2962968734 abstract "We show that Sine$_beta$, the bulk limit of the Gaussian $beta$-ensembles is the spectrum of a self-adjoint random differential operator [ fto 2 {R_t^{-1}} left[ begin{array}{cc} 0 &-tfrac{d}{dt} tfrac{d}{dt} &0 end{array} right] f, qquad f:[0,1)to mathbb R^2, ] where $R_t$ is the positive definite matrix representation of hyperbolic Brownian motion with variance $4/beta$ in logarithmic time. The result connects the Montgomery-Dyson conjecture about the Sine$_2$ process and the non-trivial zeros of the Riemann zeta function, the Hilbert-P'olya conjecture and de Brange's attempt to prove the Riemann hypothesis. We identify the Brownian carousel as the Sturm-Liouville phase function of this operator. We provide similar operator representations for several other finite dimensional random ensembles and their limits: finite unitary or orthogonal ensembles, Hua-Pickrell ensembles and their limits, hard-edge $beta$-ensembles, as well as the Schrodinger point process. In this more general setting, hyperbolic Brownian motion is replaced by a random walk or Brownian motion on the affine group. Our approach provides a unified framework to study $beta$-ensembles that has so far been missing in the literature. In particular, we connect It^o's classification of affine Brownian motions with the classification of limits of random matrix ensembles." @default.
• W2962968734 created "2019-07-30" @default.
• W2962968734 creator A5020740125 @default.
• W2962968734 creator A5075377725 @default.
• W2962968734 date "2016-12-08" @default.
• W2962968734 modified "2023-10-16" @default.
• W2962968734 title "The Sine $$_beta $$ β operator" @default.
• W2962968734 cites W1532632375 @default.
• W2962968734 cites W1535638438 @default.
• W2962968734 cites W1967334724 @default.
• W2962968734 cites W1981668128 @default.
• W2962968734 cites W1991057622 @default.
• W2962968734 cites W2007348070 @default.
• W2962968734 cites W2012617999 @default.
• W2962968734 cites W2017295671 @default.
• W2962968734 cites W2030407005 @default.
• W2962968734 cites W2049587182 @default.
• W2962968734 cites W2054352189 @default.
• W2962968734 cites W2066143814 @default.
• W2962968734 cites W2068184834 @default.
• W2962968734 cites W2070694478 @default.
• W2962968734 cites W2072534883 @default.
• W2962968734 cites W2079474739 @default.
• W2962968734 cites W2082829459 @default.
• W2962968734 cites W2083587735 @default.
• W2962968734 cites W2090455737 @default.
• W2962968734 cites W2111998221 @default.
• W2962968734 cites W2157279769 @default.
• W2962968734 cites W2168725312 @default.
• W2962968734 cites W2480353178 @default.
• W2962968734 cites W2499952289 @default.
• W2962968734 cites W2802008906 @default.
• W2962968734 cites W3098770948 @default.
• W2962968734 cites W3099505683 @default.
• W2962968734 cites W3100869531 @default.
• W2962968734 cites W3102347392 @default.
• W2962968734 cites W3104682004 @default.
• W2962968734 cites W3105737864 @default.
• W2962968734 cites W3122967342 @default.
• W2962968734 cites W4241324437 @default.
• W2962968734 cites W4244259842 @default.
• W2962968734 cites W4256206838 @default.
• W2962968734 cites W4294576855 @default.
• W2962968734 cites W653925602 @default.
• W2962968734 doi "https://doi.org/10.1007/s00222-016-0709-x" @default.
• W2962968734 hasPublicationYear "2016" @default.
• W2962968734 type Work @default.
• W2962968734 sameAs 2962968734 @default.
• W2962968734 citedByCount "19" @default.
• W2962968734 countsByYear W29629687342018 @default.
• W2962968734 countsByYear W29629687342019 @default.
• W2962968734 countsByYear W29629687342020 @default.
• W2962968734 countsByYear W29629687342021 @default.
• W2962968734 countsByYear W29629687342022 @default.
• W2962968734 countsByYear W29629687342023 @default.
• W2962968734 crossrefType "journal-article" @default.
• W2962968734 hasAuthorship W2962968734A5020740125 @default.
• W2962968734 hasAuthorship W2962968734A5075377725 @default.
• W2962968734 hasBestOaLocation W29629687342 @default.
• W2962968734 hasConcept C104317684 @default.
• W2962968734 hasConcept C105795698 @default.
• W2962968734 hasConcept C112401455 @default.
• W2962968734 hasConcept C114614502 @default.
• W2962968734 hasConcept C121332964 @default.
• W2962968734 hasConcept C134306372 @default.
• W2962968734 hasConcept C158448853 @default.
• W2962968734 hasConcept C158693339 @default.
• W2962968734 hasConcept C17020691 @default.
• W2962968734 hasConcept C185592680 @default.
• W2962968734 hasConcept C186661526 @default.
• W2962968734 hasConcept C202444582 @default.
• W2962968734 hasConcept C2524010 @default.
• W2962968734 hasConcept C2780990831 @default.
• W2962968734 hasConcept C33923547 @default.
• W2962968734 hasConcept C37914503 @default.
• W2962968734 hasConcept C55493867 @default.
• W2962968734 hasConcept C62520636 @default.
• W2962968734 hasConcept C64812099 @default.
• W2962968734 hasConcept C70915906 @default.
• W2962968734 hasConcept C72010251 @default.
• W2962968734 hasConcept C86339819 @default.
• W2962968734 hasConceptScore W2962968734C104317684 @default.
• W2962968734 hasConceptScore W2962968734C105795698 @default.
• W2962968734 hasConceptScore W2962968734C112401455 @default.
• W2962968734 hasConceptScore W2962968734C114614502 @default.
• W2962968734 hasConceptScore W2962968734C121332964 @default.
• W2962968734 hasConceptScore W2962968734C134306372 @default.
• W2962968734 hasConceptScore W2962968734C158448853 @default.
• W2962968734 hasConceptScore W2962968734C158693339 @default.
• W2962968734 hasConceptScore W2962968734C17020691 @default.
• W2962968734 hasConceptScore W2962968734C185592680 @default.
• W2962968734 hasConceptScore W2962968734C186661526 @default.
• W2962968734 hasConceptScore W2962968734C202444582 @default.
• W2962968734 hasConceptScore W2962968734C2524010 @default.
• W2962968734 hasConceptScore W2962968734C2780990831 @default.
• W2962968734 hasConceptScore W2962968734C33923547 @default.
• W2962968734 hasConceptScore W2962968734C37914503 @default.
• W2962968734 hasConceptScore W2962968734C55493867 @default.

• next