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pro vyhledávání: '"Peköz, Erol"'
In Gambler's Ruin when both players start with the same amount of money, we show the playing time stochastically increases when the games are made more fair. We give two different arguments for this fact that extend results from \cite{Pek2021}. We th
Externí odkaz:
http://arxiv.org/abs/2301.08328
Autor:
Johnson, Tobias, Peköz, Erol
Publikováno v:
Stochastic Process. Appl., 152 1-31, 2022
Generalized gamma distributions arise as limits in many settings involving random graphs, walks, trees, and branching processes. Pek\"oz, R\"ollin, and Ross (2016, arXiv:1309.4183 [math.PR]) exploited characterizing distributional fixed point equatio
Externí odkaz:
http://arxiv.org/abs/2108.02101
Autor:
Fang, Xiao, Gan, Han Liang, Holmes, Susan, Huang, Haiyan, Peköz, Erol, Röllin, Adrian, Tang, Wenpin
A classical result for the simple symmetric random walk with $2n$ steps is that the number of steps above the origin, the time of the last visit to the origin, and the time of the maximum height all have exactly the same distribution and converge whe
Externí odkaz:
http://arxiv.org/abs/2001.08857
We study occupancy counts for the critical nearest-neighbor branching random walk on the $d$-dimensional lattice, conditioned on non-extinction. For $d\geq 3$, Lalley and Zheng (2011) showed that the properly scaled joint distribution of the number o
Externí odkaz:
http://arxiv.org/abs/1909.01617
Autor:
Johnson, Tobias, Peköz, Erol
Publikováno v:
In Stochastic Processes and their Applications October 2022 152:1-31
We study the number of white balls in a classical P\'olya urn model with the additional feature that, at random times, a black ball is added to the urn. The number of draws between these random times are i.i.d. and, under certain moment conditions on
Externí odkaz:
http://arxiv.org/abs/1607.03211
Hall, Deckert and Wiseman (2014) recently proposed that quantum theory can be understood as the continuum limit of a deterministic theory in which there is a large, but finite, number of classical "worlds." A resulting Gaussian limit theorem for part
Externí odkaz:
http://arxiv.org/abs/1606.06618
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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 convergence with respect to the p-norm topology for appropriate p and also
Externí odkaz:
http://arxiv.org/abs/1402.4686
Publikováno v:
Annals of Probability 2016, Vol. 44, No. 3, 1776-1816
We study a new class of time inhomogeneous P\'olya-type urn schemes and give optimal rates of convergence for the distribution of the properly scaled number of balls of a given color to nearly the full class of generalized gamma distributions with in
Externí odkaz:
http://arxiv.org/abs/1309.4183