University of California, Davis

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20022008

most citedLieb-Robinson Bounds and the Exponential Clustering Theorem

418 citations

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14 papers · 1 filter

math.PR2008

Local Bootstrap Percolation

Janko Gravner, Alexander E. Holroyd

We study a variant of bootstrap percolation in which growth is restricted to a single active cluster. Initially there is a single active site at the origin, while other sites of Z^…

math.PR2008

Spectral gap for the interchange process in a box

Ben Morris

We show that the spectral gap for the interchange process (and the symmetric exclusion process) in a $d$ -dimensional box of side length $L$ is asymptotic to $π^{2} / L^{2}$ . This gives m…

math.PR2008★ 137 cited

A Fredholm Determinant Representation in ASEP

Craig A. Tracy, Harold Widom

In previous work the authors found integral formulas for probabilities in the asymmetric simple exclusion process (ASEP) on the integer lattice. The dynamics are uniquely determine…

math.PR2007

On the lower bound of the spectral norm of symmetric random matrices with independent entries

Sandrine Peche, Alexander Soshnikov

We show that the spectral radius of an $N \times N$ random symmetric matrix with i.i.d. bounded centered but non-symmetrically distributed entries is bounded from below by $ 2 \*σ-…

math.PR2007★ 2 cited

Wigner random matrices with non-symmetrically distributed entries

Sandrine Peche, Alexander Soshnikov

We show that the spectral radius of an $N \times N$ random symmetric matrix with i.i.d. bounded centered but non-symmetrically distributed entries is bounded from above by $ 2 \*σ+…

math.PR2005

Jacobians and rank 1 perturbations relating to unitary Hessenberg matrices

Peter J. Forrester, Eric M. Rains

In a recent work Killip and Nenciu gave random recurrences for the characteristic polynomials of certain unitary and real orthogonal upper Hessenberg matrices. The corresponding ei…