75 citations · 190 across the 7 of their papers we have counts for
9 papers
Arcsine laws for random walks generated from random permutations with applications to genomics
Xiao Fang, Han Liang Gan, Susan Holmes +4
A classical result for the simple symmetric random walk with steps is that the number of steps above the origin, the time of the last visit to the origin, and the time of the…
Exponential and Laplace approximation for occupation statistics of branching random walk
Erol Peköz, Adrian Röllin, Nathan Ross
We study occupancy counts for the critical nearest-neighbor branching random walk on the -dimensional lattice, conditioned on non-extinction. For , Lalley and Zheng (20…
Pólya urns with immigration at random times
Erol Peköz, Adrian Röllin, Nathan Ross
We study the number of white balls in a classical Pólya urn model with the additional feature that, at random times, a black ball is added to the urn. The number of draws between t…
Joint degree distributions of preferential attachment random graphs
Erol A. Peköz, Adrian Röllin, Nathan Ross
We study the joint degree counts in proportional attachment random graphs and find a simple representation for the limit distribution in infinite sequence space. We show weak conve…
Generalized gamma approximation with rates for urns, walks and trees
Erol A. Peköz, Adrian Röllin, Nathan Ross
We study a new class of time inhomogeneous Pólya-type urn schemes and give optimal rates of convergence for the distribution of the properly scaled number of balls of a given color…
Degree asymptotics with rates for preferential attachment random graphs
Erol A. Peköz, Adrian Röllin, Nathan Ross
We provide optimal rates of convergence to the asymptotic distribution of the (properly scaled) degree of a fixed vertex in two preferential attachment random graph models. Our app…
Total variation error bounds for geometric approximation
Erol A. Peköz, Adrian Röllin, Nathan Ross
We develop a new formulation of Stein's method to obtain computable upper bounds on the total variation distance between the geometric distribution and a distribution of interest.…
New rates for exponential approximation and the theorems of Rényi and Yaglom
Erol A. Peköz, Adrian Röllin
We introduce two abstract theorems that reduce a variety of complex exponential distributional approximation problems to the construction of couplings. These are applied to obtain…
A Three-Parameter Binomial Approximation
Vydas Čekanavičius, Erol A. Peköz, Adrian Röllin +1
We approximate the distribution of the sum of independent but not necessarily identically distributed Bernoulli random variables using a shifted binomial distribution where the thr…