Negative dependence and the geometry of polynomials
DOI10.1090/S0894-0347-08-00618-8zbMath1206.62096arXiv0707.2340OpenAlexW2008095352MaRDI QIDQ3079205
Petter Brändén, Thomas M. Liggett, Julius Borcea
Publication date: 2 March 2011
Published in: Journal of the American Mathematical Society (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/0707.2340
determinantsmatricesmatroidsprobability measuresinteracting particle systemsnegative associationexclusion processesstochastic dominationspanning treeshyperbolic polynomialsstable polynomials
Measures of association (correlation, canonical correlation, etc.) (62H20) Characterization and structure theory for multivariate probability distributions; copulas (62H05) Probability distributions: general theory (60E05) Interacting random processes; statistical mechanics type models; percolation theory (60K35)
Related Items
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Local characteristics, entropy and limit theorems for spanning trees and domino tilings via transfer-impedances
- The Lee--Yang and Pólya--Schur programs. I: Linear operators preserving stability
- Determinantal processes with number variance saturation
- Jensen polynomials and the Turán and Laguerre inequalities
- Applications of stable polynomials to mixed determinants: Johnson's conjectures, unimodality, and symmetrized Fischer products
- Negatively correlated random variables and Mason's conjecture for independent sets in matroids
- Determinantal processes and independence
- Distributional limits for the symmetric exclusion process
- Spectral order and isotonic differential operators of Laguerre-Pólya type
- A correlation inequality for the symmetric exclusion process
- Normal fluctuations and the FKG inequalities
- An introduction to the theory of point processes
- Correlation inequalities on some partially ordered sets
- Open problems on GKK \(\tau\)-matrices
- Ultra logconcave sequences and negative dependence
- Stationary determinantal processes: phase multiplicity, Bernoullicity, entropy, and domination
- Homogeneous multivariate polynomials with the half-plane property
- Matroid inequalities from electrical network theory
- The influence of variables in product spaces
- Negative association of random variables, with applications
- Determinantal probability measures
- Random-cluster measures and uniform spanning trees
- Pólya-Schur master theorems for circular domains and their boundaries
- Polynomials with the half-plane property and matroid theory
- Hyperdeterminantal relations among symmetric principal minors
- Lacunas for hyperbolic differential operators with constant coefficients. II
- On the generating functions of totally positive sequences. I
- Hyperbolic Polynomials and Convex Analysis
- Towards a theory of negative dependence
- Probability on Trees and Networks
- Hyperbolic polynomials approach to Van der Waerden/Schrijver-Valiant like conjectures
- Negative correlation and log-concavity
- Rayleigh Matroids
- Positive Influence and Negative Dependence
- Multivariate Pólya-Schur classification problems in the Weyl algebra
- The Lee‐Yang and Pólya‐Schur programs. II. Theory of stable polynomials and applications
- A Combinatorial Proof of the All Minors Matrix Tree Theorem
- Combinatorial applications of an inequality from statistical mechanics
- Generalized Matrix Function Inequalities on M-Matrices
- Hyperbolic Polynomials and Interior Point Methods for Convex Programming
- Balls and bins: A study in negative dependence
- Correlation function of Schur process with application to local geometry of a random 3-dimensional Young diagram
- $M$-matrices satisfy Newton’s inequalities
- Asymptotics of Plancherel measures for symmetric groups
- Negative Association Does not Imply Log-Concavity of the Rank Sequence
- The Random-Cluster Model
- Weakly sign-symmetric matrices and some determinantal inequalities
- Inequalities: theory of majorization and its applications
- Notions of convexity
- Discrete orthogonal polynomial ensembles and the Plancherel measure