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11 papers · 1 filter
On adding a list of numbers (and other one-dependent determinantal processes)
Alexei Borodin, Persi Diaconis, Jason Fulman
Adding a column of numbers produces "carries" along the way. We show that random digits produce a pattern of carries with a neat probabilistic description: the carries form a one-d…
Singularity sets of Levy processes
Arnaud Durand
We completely describe the size and large intersection properties of the Holder singularity sets of Levy processes. We also study the set of times at which a given function cannot…
Observability and nonlinear filtering
Ramon van Handel
This paper develops a connection between the asymptotic stability of nonlinear filters and a notion of observability. We consider a general class of hidden Markov models in continu…
Stochastic Variational Integrators
Nawaf Bou-Rabee, Houman Owhadi
This paper presents a continuous and discrete Lagrangian theory for stochastic Hamiltonian systems on manifolds. The main result is to derive stochastic governing equations for suc…
Infinite-dimensional diffusions as limits of random walks on partitions
Alexei Borodin, Grigori Olshanski
The present paper originated from our previous study of the problem of harmonic analysis on the infinite symmetric group. This problem leads to a family {P_z} of probability measur…
Asymptotics of Plancherel-type random partitions
Alexei Borodin, Grigori Olshanski
We present a solution to a problem suggested by Philippe Biane: We prove that a certain Plancherel-type probability distribution on partitions converges, as partitions get large, t…