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Large deviations and overflow probabilities for the general single-server queue, with applications
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
Directed polymers and the quantum Toda lattice
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
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
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
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
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
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
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
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