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Large deviations and overflow probabilities for the general single-server queue, with applications
- N. Duffield, N. O'Connell
- Mathematics
- 1 September 1995
We consider queueing systems where the workload process is assumed to have an associated large deviation principle with arbitrary scaling: there exist increasing scaling functions (at,vt,teE+) and a…
Brownian analogues of Burke's theorem
- N. O'Connell, M. Yor
- Mathematics
- 1 December 2001
Directed polymers and the quantum Toda lattice
- N. O'Connell
- Mathematics
- 1 October 2009
We characterize the law of the partition function of a Brownian directed polymer model in terms of a diffusion process associated with the quantum Toda lattice. The proof is via a multidimensional…
A Representation for Non-Colliding Random Walks
- N. O'Connell, M. Yor
- Mathematics
- 2002
We define a sequence of mappings $\Gamma_k:D_0(R_+)^k\to D_0(R_+)^k$ and prove the following result: Let $N_1,\ldots,N_n$ be the counting functions of independent Poisson processes on $R_+$ with…
Littelmann paths and Brownian paths
- P. Biane, P. Bougerol, N. O'Connell
- Mathematics
- 10 March 2004
We study some path transformations related to Littelmann path model and their applications to representation theory and Brownian motion in a Weyl chamber.
On the Characteristic Polynomial¶ of a Random Unitary Matrix
- C. Hughes, J. Keating, N. O'Connell
- Mathematics
- 1 July 2001
Abstract: We present a range of fluctuation and large deviations results for the logarithm of the characteristic polynomial Z of a random N×N unitary matrix, as N→∞. First we show that , evaluated at…
Non-Colliding Random Walks, Tandem Queues, and DiscreteOrthogonal Polynomial Ensembles
- W. König, N. O'Connell, S. Roch
- Mathematics
- 2002
We show that the function $h(x)=\prod_{i < j}(x_j-x_i)$ is harmonic for any random walk in $R^k$ with exchangeable increments, provided the required moments exist. For the subclass of random walks…
Conditioned random walks and the RSK correspondence
- N. O'Connell
- Mathematics
- 28 March 2003
We consider the stochastic evolution of three variants of the RSK algorithm, giving both analytic descriptions and probabilistic interpretations. Symmetric functions play a key role, and the…
A path-transformation for random walks and the Robinson-Schensted correspondence
- N. O'Connell
- Mathematics
- 18 March 2002
The author and Marc Yor recently introduced a path-transformation G((k)) with the property that, for X belonging to a certain class of random walks on Z(+)(k), the transformed walk G((k))( X) has the…
Eigenvalues of the Laguerre Process as Non-Colliding Squared Bessel Processes
- W. König, N. O'Connell
- Mathematics
- 31 August 2001
Let $A(t)$ be an $n\times p$ matrix with independent standard complex Brownian entries and set $M(t)=A(t)^*A(t)$. This is a process version of the Laguerre ensemble and as such we shall refer to it…
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