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Hooghiemstra, G. (author), Van Mieghem, P. (author)In this article Gerard Hooghiemstra and Piet van Mieghem explain why the Gauss inequality is overshadowed by the Chebychev inequality. Furthermore, they present a proof of the Gauss inequality in modern notation.journal article 2015
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- Bhamidi, S. (author), Van der Hofstad, R. (author), Hooghiemstra, G. (author) journal article 2011
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- Bhamidi, S. (author), Van der Hofstad, R. (author), Hooghiemstra, G. (author) journal article 2010
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Bhamidi, S. (author), Van der Hofstad, R. (author), Hooghiemstra, G. (author)We study first passage percolation (FPP) on the configuration model (CM) having power-law degrees with exponent ? ? [1, 2) and exponential edge weights. We derive the distributional limit of the minimal weight of a path between typical vertices in the network and the number of edges on the minimal-weight path, both of which can be computed in...journal article 2010
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Dommers, S. (author), Van der Hofstad, R. (author), Hooghiemstra, G. (author)In this paper, we investigate the diameter in preferential attachment (PA-) models, thus quantifying the statement that these models are small worlds. The models studied here are such that edges are attached to older vertices proportional to the degree plus a constant, i.e., we consider affine PA-models. There is a substantial amount of...journal article 2010
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Van der Hofstad, R. (author), Hooghiemstra, G. (author)We survey the recent work on phase transition and distances in various random graph models with general degree sequences. We focus on inhomogeneous random graphs, the configuration model, and affine preferential attachment models, and pay special attention to the setting where these random graphs have a power-law degree sequence. This means that...journal article 2008
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Van den Esker, H. (author), Van der Hofstad, R. (author), Hooghiemstra, G. (author)We generalize the asymptotic behavior of the graph distance between two uniformly chosen nodes in the configuration model to a wide class of random graphs. Among others, this class contains the Poissonian random graph, the expected degree random graph and the generalized random graph (including the classical Erdos-Renyi graph). In the paper we...journal article 2008
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Deijfen, M. (author), Van den Esker, H. (author), Van der Hofstad, R. (author), Hooghiemstra, G. (author)In this paper, a random graph process {G(t)} (ta parts per thousand yen1) is studied and its degree sequence is analyzed. Let {W (t) } (ta parts per thousand yen1) be an i.i.d. sequence. The graph process is defined so that, at each integer time t, a new vertex with W (t) edges attached to it, is added to the graph. The new edges added at time t...journal article 2008
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Van der Hofstad, R. (author), Hooghiemstra, G. (author), Van Mieghem, P. (author)The minimal weight of the shortest path tree in a complete graph with independent and exponential (mean 1) random link weights, is shown to converge to a Gaussian distribution. We prove a conditional central limit theorem and show that the condition holds with probability converging to 1.conference paper 2007
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Van der Hofstad, R. (author), Hooghiemstra, G. (author), Znamenski, D. (author)In this paper, we study the configuration model (CM) with independent and identically-distributed (i.i.d.) degrees. We establish a phase transition for the diameter when the power-law exponent ? of the degrees satisfies ? ? (2, 3). Indeed, we show that for ? > 2 and when vertices with degree 1 or 2 are present with positive probability, the...journal article 2007
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Van der Hofstad, R. (author), Hooghiemstra, G. (author), Van Mieghem, P. (author)We derive the distribution of the number of links and the average weight for the shortest path tree (SPT) rooted at an arbitrary node to m uniformly chosen nodes in the complete graph of size N with i.i.d. exponential link weights. We rely on the fact that the full shortest path tree to all destinations (i.e., m = N ? 1) is a uniform recursive...conference paper 2006
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- van Mieghem, P. (author), Hooghiemstra, G. (author), van der Hofstad, R.W. (author) report 2002
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Goverde, R.M.P. (author), Hansen, I.A. (author), Hooghiemstra, G. (author), Lopuhaa, H.P. (author)The estimation of the precise arrival and departure times of trains at stations is done by means of a software tool that extracts the occupation and clearance times of each train per track section of the Dutch Railways‘ network. The software tool was applied to the whole automatically collected set of signal data of the area of Eindhoven during...conference paper 2001
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- Van Mieghem, P. (author), Hooghiemstra, G. (author), van der Hofstad, R. (author) journal article 2001
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- Hooghiemstra, G. (author), van Mieghem, P. (author) report 2001
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- van Mieghem, P. (author), Hooghiemstra, G. (author), van der Hofstad, R. (author) report 2000
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Hooghiemstra, G. (author), Groeneboom, P. (author), Lopuhaa, P. (author)Groeneboom introduced a jump process that can be used (among other things) to study the asymptotic properties of the Grenander estimator of a monotone density. In this paper we derive the asymptotic normality of a suitably rescaled version of the $L_1$ error of the Grenander estimator, using properties of this jump process.journal article 1999
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- De Kort, A.F. (author), Heidergott, B. (author), Van Egmond, R.J. (author), Hooghiemstra, G. (author) book 1999
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Hooghiemstra, G. (author), Greenwood, P.E. (author)Let be a sequence of independent random variables with common distribution and define the iteration , , . We denote by the domain of maximal attraction of , the extreme value distribution of the first type. Greenwood and Hooghiemstra showed in 1991 that for there exist norming constants and such that has a non-degenerate (distributional) limit....journal article 1996
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- Olsder, G.J. (author), Resing, J.A.C. (author), De Vries, R.E. (author), Keane, M.S. (author), Hooghiemstra, G. (author) journal article 1990
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