FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W1953261036> ?p ?o ?g. }

• W1953261036 abstract "We consider higher-dimensional generalizations of the normalized Laplacian and the adjacency matrix of graphs and study their eigenvalues for the Linial-Meshulam model $X^k(n,p)$ of random $k$-dimensional simplicial complexes on $n$ vertices. We show that for $p=Omega(log n/n)$, the eigenvalues of these matrices are a.a.s. concentrated around two values. The main tool, which goes back to the work of Garland, are arguments that relate the eigenvalues of these matrices to those of graphs that arise as links of $(k-2)$-dimensional faces. Garland's result concerns the Laplacian; we develop an analogous result for the adjacency matrix. The same arguments apply to other models of random complexes which allow for dependencies between the choices of $k$-dimensional simplices. In the second part of the paper, we apply this to the question of possible higher-dimensional analogues of the discrete Cheeger inequality, which in the classical case of graphs relates the eigenvalues of a graph and its edge expansion. It is very natural to ask whether this generalizes to higher dimensions and, in particular, whether the higher-dimensional Laplacian spectra capture the notion of coboundary expansion - a generalization of edge expansion that arose in recent work of Linial and Meshulam and of Gromov. We show that this most straightforward version of a higher-dimensional discrete Cheeger inequality fails, in quite a strong way: For every $kgeq 2$ and $nin mathbb{N}$, there is a $k$-dimensional complex $Y^k_n$ on $n$ vertices that has strong spectral expansion properties (all nontrivial eigenvalues of the normalised $k$-dimensional Laplacian lie in the interval $[1-O(1/sqrt{n}),1+O(1/sqrt{n})]$) but whose coboundary expansion is bounded from above by $O(log n/n)$ and so tends to zero as $nrightarrow infty$; moreover, $Y^k_n$ can be taken to have vanishing integer homology in dimension less than $k$." @default.
• W1953261036 created "2016-06-24" @default.
• W1953261036 creator A5056297132 @default.
• W1953261036 creator A5074677644 @default.
• W1953261036 date "2014-11-18" @default.
• W1953261036 modified "2023-09-27" @default.
• W1953261036 title "On Eigenvalues of Random Complexes" @default.
• W1953261036 cites W100944330 @default.
• W1953261036 cites W1530355788 @default.
• W1953261036 cites W1565832774 @default.
• W1953261036 cites W1600293573 @default.
• W1953261036 cites W1603500723 @default.
• W1953261036 cites W1631603072 @default.
• W1953261036 cites W1664849218 @default.
• W1953261036 cites W1698477647 @default.
• W1953261036 cites W1699054086 @default.
• W1953261036 cites W1863203090 @default.
• W1953261036 cites W1876101497 @default.
• W1953261036 cites W1970176528 @default.
• W1953261036 cites W1978238050 @default.
• W1953261036 cites W1993111701 @default.
• W1953261036 cites W2002243081 @default.
• W1953261036 cites W2002374042 @default.
• W1953261036 cites W2018047324 @default.
• W1953261036 cites W2018582120 @default.
• W1953261036 cites W2021145763 @default.
• W1953261036 cites W2025796118 @default.
• W1953261036 cites W2026709222 @default.
• W1953261036 cites W2029673229 @default.
• W1953261036 cites W2030214687 @default.
• W1953261036 cites W2036878392 @default.
• W1953261036 cites W2038098381 @default.
• W1953261036 cites W2045377861 @default.
• W1953261036 cites W2048958388 @default.
• W1953261036 cites W2052852732 @default.
• W1953261036 cites W2060103041 @default.
• W1953261036 cites W2068537642 @default.
• W1953261036 cites W2073443682 @default.
• W1953261036 cites W2088164510 @default.
• W1953261036 cites W2089096000 @default.
• W1953261036 cites W2090464710 @default.
• W1953261036 cites W2095087473 @default.
• W1953261036 cites W2106079666 @default.
• W1953261036 cites W2109286989 @default.
• W1953261036 cites W2112643910 @default.
• W1953261036 cites W2125511726 @default.
• W1953261036 cites W2132890668 @default.
• W1953261036 cites W2134506831 @default.
• W1953261036 cites W2153710291 @default.
• W1953261036 cites W2168034769 @default.
• W1953261036 cites W2177539811 @default.
• W1953261036 cites W2187218268 @default.
• W1953261036 cites W2610857016 @default.
• W1953261036 cites W2616697817 @default.
• W1953261036 cites W2962885031 @default.
• W1953261036 cites W2963121792 @default.
• W1953261036 cites W2963986398 @default.
• W1953261036 cites W3105794348 @default.
• W1953261036 cites W3144881883 @default.
• W1953261036 cites W4882049 @default.
• W1953261036 cites W634962210 @default.
• W1953261036 cites W1771295855 @default.
• W1953261036 cites W194186055 @default.
• W1953261036 hasPublicationYear "2014" @default.
• W1953261036 type Work @default.
• W1953261036 sameAs 1953261036 @default.
• W1953261036 citedByCount "2" @default.
• W1953261036 countsByYear W19532610362015 @default.
• W1953261036 crossrefType "posted-content" @default.
• W1953261036 hasAuthorship W1953261036A5056297132 @default.
• W1953261036 hasAuthorship W1953261036A5074677644 @default.
• W1953261036 hasConcept C106487976 @default.
• W1953261036 hasConcept C110484373 @default.
• W1953261036 hasConcept C114614502 @default.
• W1953261036 hasConcept C115178988 @default.
• W1953261036 hasConcept C118615104 @default.
• W1953261036 hasConcept C121332964 @default.
• W1953261036 hasConcept C132525143 @default.
• W1953261036 hasConcept C134306372 @default.
• W1953261036 hasConcept C158693339 @default.
• W1953261036 hasConcept C159985019 @default.
• W1953261036 hasConcept C165700671 @default.
• W1953261036 hasConcept C177148314 @default.
• W1953261036 hasConcept C180356752 @default.
• W1953261036 hasConcept C192562407 @default.
• W1953261036 hasConcept C33923547 @default.
• W1953261036 hasConcept C62520636 @default.
• W1953261036 hasConcept C64812099 @default.
• W1953261036 hasConceptScore W1953261036C106487976 @default.
• W1953261036 hasConceptScore W1953261036C110484373 @default.
• W1953261036 hasConceptScore W1953261036C114614502 @default.
• W1953261036 hasConceptScore W1953261036C115178988 @default.
• W1953261036 hasConceptScore W1953261036C118615104 @default.
• W1953261036 hasConceptScore W1953261036C121332964 @default.
• W1953261036 hasConceptScore W1953261036C132525143 @default.
• W1953261036 hasConceptScore W1953261036C134306372 @default.
• W1953261036 hasConceptScore W1953261036C158693339 @default.
• W1953261036 hasConceptScore W1953261036C159985019 @default.
• W1953261036 hasConceptScore W1953261036C165700671 @default.
• W1953261036 hasConceptScore W1953261036C177148314 @default.

• next