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Discrete Polynuclear Growth and Determinantal processes
 Comm. Math. Phys
, 2003
"... Abstract. We consider a discrete polynuclear growth (PNG) process and prove a functional limit theorem for its convergence to the Airy process. This generalizes previous results by Prähofer and Spohn. The result enables us to express the F1 GOE TracyWidom distribution in terms of the Airy process. ..."
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Cited by 171 (11 self)
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Abstract. We consider a discrete polynuclear growth (PNG) process and prove a functional limit theorem for its convergence to the Airy process. This generalizes previous results by Prähofer and Spohn. The result enables us to express the F1 GOE TracyWidom distribution in terms of the Airy process. We also show some results and give a conjecture about the transversal fluctuations in a point to line last passage percolation problem. 1. Introduction and
On the determinantal representation . . .
, 2009
"... Let M be a d×d matrix whose entries are linear forms in the homogeneous coordinates of 2. Then M is called a determinantal representation of the curve {det(M) = 0}. Such representations are well studied for smooth curves. We study determinantal representations of curves with arbitrary singulariti ..."
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Cited by 1 (0 self)
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Let M be a d×d matrix whose entries are linear forms in the homogeneous coordinates of 2. Then M is called a determinantal representation of the curve {det(M) = 0}. Such representations are well studied for smooth curves. We study determinantal representations of curves with arbitrary
OBSTRUCTIONS TO DETERMINANTAL REPRESENTABILITY
, 2010
"... There has recently been ample interest in the question of which sets can be represented by linear matrix inequalities (LMIs). A necessary condition is that the set is rigidly convex, and it has been conjectured that rigid convexity is also sufficient. To this end Helton and Vinnikov conjectured th ..."
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Cited by 24 (2 self)
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that any real zero polynomial admits a determinantal representation with symmetric matrices. We disprove this conjecture. By relating the question of finding LMI representations to the problem of determining whether a polymatroid is representable over the complex numbers, we find a real zero polynomial
Dimension of families of determinantal schemes
, 2002
"... A scheme X ⊂ P n+c of codimension c is called standard determinantal if its homogeneous saturated ideal can be generated by the maximal minors of a homogeneous t×(t+c−1) matrix and X is said to be good determinantal if it is standard determinantal and a generic complete intersection. Given integers ..."
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Cited by 11 (6 self)
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homogeneous polynomial of degree aj − bi. In this paper we address the following three fundamental problems: To determine (1) the dimension of W(b; a) (resp. Ws(b; a)) in terms of aj and bi, (2) whether the closure of W(b; a) is an irreducible component of Hilb p (P n+c), and (3) when Hilb p (P n
Resultants of Determinantal Varieties
, 2004
"... In this paper, a new kind of resultant, called the determinantal resultant, is introduced. This operator computes the projection of a determinantal variety under suitable hypothesis. As a direct generalization of the resultant of a very ample vector bundle [GKZ94], it corresponds to a necessary and ..."
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Cited by 8 (4 self)
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In this paper, a new kind of resultant, called the determinantal resultant, is introduced. This operator computes the projection of a determinantal variety under suitable hypothesis. As a direct generalization of the resultant of a very ample vector bundle [GKZ94], it corresponds to a necessary
Determinantal processes and independence
, 2006
"... We give a probabilistic introduction to determinantal and permanental point processes. Determinantal processes arise in physics (fermions, eigenvalues of random matrices) and in combinatorics (nonintersecting paths, random spanning trees). They have the striking property that the number of points i ..."
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Cited by 20 (1 self)
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We give a probabilistic introduction to determinantal and permanental point processes. Determinantal processes arise in physics (fermions, eigenvalues of random matrices) and in combinatorics (nonintersecting paths, random spanning trees). They have the striking property that the number of points
Resultants of determinantal varieties
"... In this paper, a new kind of resultant, called the determinantal resultant, is introduced. This operator computes the projection of a determinantal variety under suitable hypothesis. As a direct generalization of the resultant of a very ample vector bundle [GKZ94], it corresponds to a necessary an ..."
Abstract
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In this paper, a new kind of resultant, called the determinantal resultant, is introduced. This operator computes the projection of a determinantal variety under suitable hypothesis. As a direct generalization of the resultant of a very ample vector bundle [GKZ94], it corresponds to a necessary
ON A DETERMINANTAL FORMULA OF TADIĆ
"... Abstract. We study a special class of irreducible representations of GLn over a local nonArchimedean field which we call ladder representations. This is a natural class in the admissible dual which contains the Speh representations. We show that the Tadić determinantal formula is valid for this cla ..."
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Cited by 7 (0 self)
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Abstract. We study a special class of irreducible representations of GLn over a local nonArchimedean field which we call ladder representations. This is a natural class in the admissible dual which contains the Speh representations. We show that the Tadić determinantal formula is valid
Gröbner bases and determinantal ideals
 COMMUTATIVE ALGEBRA, SINGULARITIES AND COMPUTER ALGEBRA
, 2003
"... We give an introduction to the theory of determinantal ideals and rings, their Gröbner bases, initial ideals and algebras, respectively. The approach is based on the straightening law and the KnuthRobinsonSchensted correspondence. The article contains a section treating the basic results about th ..."
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Cited by 5 (3 self)
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We give an introduction to the theory of determinantal ideals and rings, their Gröbner bases, initial ideals and algebras, respectively. The approach is based on the straightening law and the KnuthRobinsonSchensted correspondence. The article contains a section treating the basic results about
Results 1  10
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