92 research outputs found
The mobile Boolean model: an overview and further results
No full textThis paper offers an overview of the mobile Boolean stochastic geometric model which is a time-dependent version of the ordinary Boolean model in a Euclidean space of dimension d. The main question asked is that of obtaining the law of the detection time of a fixed set. We give various ways of thinking about this which result into some general formulas. The formulas are solvable in some special cases, such the inertial and Brownian mobile Boolean models. In the latter case, we obtain some expressions for the distribution of the detection time of a ball, when the dimension d is odd and asymptotics when d is even. Finally, we pose some questions for future research
Limit theorems for a random directed slab graph
No full textWe consider a stochastic directed graph on the integers whereby a directed
edge between and a larger integer exists with probability
depending solely on the distance between the two integers. Under broad
conditions, we identify a regenerative structure that enables us to prove limit
theorems for the maximal path length in a long chunk of the graph. The model is
an extension of a special case of graphs studied by Foss and Konstantopoulos,
Markov Process and Related Fields, 9, 413-468. We then consider a similar type
of graph but on the `slab' , where is a finite partially
ordered set. We extend the techniques introduced in the in the first part of
the paper to obtain a central limit theorem for the longest path. When is
linearly ordered, the limiting distribution can be seen to be that of the
largest eigenvalue of a random matrix in the Gaussian unitary
ensemble (GUE)
Alumni Author 2016
No full textAlumni author Nicky P.E. Tomboulides shared her book, It Is a Green Clean World: The World Travels of Takis and Mimi, Ryan Matura Library September 17, 2016.https://digitalcommons.sacredheart.edu/libraryhistoryphotos/1085/thumbnail.jp
Alumni Author Nicky P.E. Tomboulides
No full textSacred Heart University\u27s Office of Alumni Engagement hosted an Alumni Author Spotlight on September 17, 2016 at RML. It Is a Green Clean World: The World Travels of Takis and Mimi by alumni author Nicky P.E. Tomboulides.https://digitalcommons.sacredheart.edu/libraryhistoryphotos/1084/thumbnail.jp
A review of Burke's theorem for Brownian motion
No full textBurke's theorem is a well-known fundamental result in queueing theory, stating that a stationary M/M/1 queue has a departure process that is identical in law to the arrival process and, moreover, for each time t, the following three random objects are independent: the queue length at time t, the arrival process after t and the departure process before t. Burke's theorem also holds for a stationary Brownian queue. In particular, it implies that a certain "complicated" functional derived from two independent Brownian motions is also a Brownian motion. The aim of this overview paper is to present an independent complete explanation of this phenomenon.</p
A multilinear algebra proof of the Cauchy-Binet formula and a multilinear version of Parseval's identity
No full textWe give a short proof of the Cauchy-Binet determinantal formula using
multilinear algebra by first generalizing it to an identity {\em not} involving
determinants. By extending the formula to abstract Hilbert spaces we obtain, as
a corollary, a generalization of the classical Parseval identity
A PROBABILISTIC INTERPRETATION OF THE GAUSSIAN BINOMIAL COEFFICIENTS
No full textWe present a stand-alone simple proof of a probabilistic interpretation of the Gaussian binomial coefficients by conditioning a random walk to hit a given lattice point at a given time
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