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COUNTING THE FACES OF RANDOMLY-PROJECTED HYPERCUBES AND ORTHANTS, WITH APPLICATIONS
RANDOMLY-PROJECTED ORTHANTS
2015/8/21
Let RN
+ denote the positive orthant; the expected number of k-faces of
the random cone ARN
+ obeys Efk(ARN
+)/fk(RN
+) = 1 − PN−n,N−k. The
formula applies to numerous matrix e...
COUNTING FACES OF RANDOMLY-PROJECTED POLYTOPES WHEN THE PROJECTION RADICALLY LOWERS DIMENSION
RANDOMLY-PROJECTED RADICALLY LOWERS DIMENSION
2015/8/21
The modern trend in statistics and probability is to consider the case where both
the number of dimensions d and the sample size n are large [19, 21]. In that case, the
intuition fostered by the cla...
Neighborliness of Randomly-Projected Simplices in High Dimensions
Neighborly Polytopes Convex Hull of Gaussian Sample
2015/8/21
Let A be a d by n matrix, d < n. Let T = T
n−1 be the standard regular simplex in R
n
.
We count the faces of the projected simplex AT in the case where the projection is random,
the dimens...
POWER LAWS FOR MONKEYS TYPINGS RANDOMLY: THE CASE OF UNEQUAL PROBABILITIES
TYPINGS RANDOMLY UNEQUAL PROBABILITIES
2015/7/6
The case where letters are hit with unequal probability has been the subject of recent confusion, with
some suggesting that in this case the rank-frequency distribution follows a lognormal distributi...
The Poincare map of randomly perturbed periodic motion
Poincare map random perturbations limit cycle Dynamical Systems
2012/6/15
A system of autonomous differential equations with a stable limit cycle and perturbed by small white noise is analyzed in this work. In the vicinity of the limit cycle of the unperturbed deterministic...
Flying randomly in $\mathbb{R}^d$ with Dirichlet displacements
Bessel functions Dirichlet distributions fractional Poisson process Mittag-Leer functions hyperspherical coordinates
2011/9/23
Abstract: Random flights in $\mathbb{R}^d,d\geq 2,$ with Dirichlet-distributed displacements and uniformly distributed orientation are analyzed. The explicit characteristic functions of the position $...
Travelling Randomly on the Poincaré Half-Plane with a Pythagorean Compass
Random motions Poisson process telegraph process hyperbolic and spherical trigonometry
2011/9/20
Abstract: A random motion on the Poincar\'e half-plane is studied. A particle runs on the geodesic lines changing direction at Poisson-paced times. The hyperbolic distance is analyzed, also in the cas...
Randomly Stopped Nonlinear Fractional Birth Processes
Fractional nonlinear pure birth processes Subordination fistable subordinator Fractional derivative First-passage time
2011/9/8
Abstract: We present and analyse the nonlinear classical pure birth process $\mathpzc{N} (t)$, $t>0$, and the fractional pure birth process $\mathpzc{N}^\nu (t)$, $t>0$, subordinated to various random...
Classical and quantum behavior of the integrated density of states for a randomly perturbed lattice
Classical quantum behavior integrated density of states randomly perturbed lattice
2011/1/20
The asymptotic behavior of the integrated density of states for a randomly perturbed lattice at the infimum of the spectrum is investigated. The leading term is determined when the decay of the single...
Let $\{X_t, t \geq 1\}$ be a sequence of identically distributed and pairwise asymptotically independent random variables with regularly varying tails and $\{ \Theta_t, t\geq1 \}$ be a sequence of pos...
We introduce a class of Kac-like kinetic equations on the real line, with general random collisional rules, which include as particular cases models for wealth redistribution in an agent-based market ...
The Advanced Encryption Standard (AES) is widely recognized as the most important block cipher in common use nowadays. This high assurance in AES is given by its resistance to ten years of extensive ...
Let G be a graph with vertex set V(G) and edge set E(G) and let g and f be two integer-valued functions defined on V(G) such that 2k m 2 h f(x) for all x ] V(G). Let H be a subgraph of G with mk edges...