| 1. |
- Alm, Sven Erick, et al.
(författare)
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A Counter-Intuitive Correlation in a Random Tournament
- 2011
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Ingår i: Combinatorics, probability & computing. - 0963-5483 .- 1469-2163. ; 20:1, s. 1-9
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Tidskriftsartikel (refereegranskat)abstract
- Consider a randomly oriented graph G = (V, E) and let a, s and b be three distinct vertices in V. We study the correlation between the events {a -> s} and {s -> b}. We show that, counter-intuitively, when G is the complete graph K-n, n >= 5, then the correlation is positive. (It is negative for n = 3 and zero for n = 4.) We briefly discuss and pose problems for the same question on other graphs.
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| 2. |
- Alm, Sven Erick
(författare)
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Approximation and Simulation of the Distributions of Scan Statistics for Poisson Processes in Higher Dimensions
- 1998
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Ingår i: Extremes. ; 1, s. 111-126
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Tidskriftsartikel (refereegranskat)abstract
- Given a Poisson process in two or three dimensions we are interested in the scan statistic, i.e. the largest number of points contained in a translate of a fixed scanning set restricted to lie inside a rectangular area.The distribution of the scan statistic is accurately approximated for rectangular scanning sets, using a technique that is also extended to higher dimensions.The accuracy of the approximation is checked through simulation.
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| 3. |
- Alm, Sven Erick, et al.
(författare)
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Bounds for the connective constant of the hexagonal lattice
- 2004
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Ingår i: J.\ Phys. A: Math. Gen.. - : IOP Publishing. ; 37, s. 549-
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Tidskriftsartikel (refereegranskat)abstract
- We give improved bounds for the connective constant of the hexagonal lattice. The lower bound is found by using Kesten's method of irreducible bridges and by determining generating functions for bridges on one-dimensional lattices.The upper bound is obtained as the largest eigenvalue of a certain transfer matrix. Using a relation between the hexagonal and the $(3.12^2)$ lattices, we also give bounds for the connective constant of the latter lattice.
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| 4. |
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| 5. |
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| 6. |
- Alm, Sven Erick, et al.
(författare)
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Correlations for Paths in Random Orientations of G(n, p) and G(n, m)
- 2011
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Ingår i: Random structures & algorithms (Print). - : Wiley. - 1042-9832 .- 1098-2418. ; 39:4, s. 486-506
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Tidskriftsartikel (refereegranskat)abstract
- We study random graphs, both G(n, p) and G(n, m), with random orientations on the edges. For three fixed distinct vertices s, a, b we study the correlation, in the combined probability space, of the events {a -> s} and {s -> b}. For G(n, p), we prove that there is a p(c) = 1/2 such that for a fixed p < p(c) the correlation is negative for large enough n and for p > p(c) the correlation is positive for large enough n. We conjecture that for a fixed n >= 27 the correlation changes sign three times for three critical values of p. For G(n, m) it is similarly proved that, with p = m/((n)(2)), there is a critical p(c) that is the solution to a certain equation and approximately equal to 0.7993. A lemma, which computes the probability of non existence of any l directed edges in G(n, m), is thought to be of independent interest. We present exact recursions to compute P(a -> s) and P(a -> s, s -> b). We also briefly discuss the corresponding question in the quenched version of the problem.
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| 8. |
- Alm, Sven Erick, et al.
(författare)
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First critical probability for a problem on random orientations in G(n,p)
- 2014
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Ingår i: Electronic Journal of Probability. - 1083-6489. ; 19, s. 69-
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Tidskriftsartikel (refereegranskat)abstract
- We study the random graph G (n,p) with a random orientation. For three fixed vertices s, a, b in G(n,p) we study the correlation of the events {a -> s} (there exists a directed path from a to s) and {s -> b}. We prove that asymptotically the correlation is negative for small p, p < C-1/n, where C-1 approximate to 0.3617, positive for C-1/n < p < 2/n and up to p = p(2)(n). Computer aided computations suggest that p(2)(n) = C-2/n, with C-2 approximate to 7.5. We conjecture that the correlation then stays negative for p up to the previously known zero at 1/2; for larger p it is positive.
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| 9. |
- Alm, Sven Erick, et al.
(författare)
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First Passage Percolation on \(\mathbb {Z}^2\) : A Simulation Study
- 2015
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Ingår i: Journal of statistical physics. - : Springer Science and Business Media LLC. - 0022-4715 .- 1572-9613. ; 161:3, s. 657-678
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Tidskriftsartikel (refereegranskat)abstract
- First passage percolation on is a model for describing the spread of an infection on the sites of the square lattice. The infection is spread via nearest neighbor sites and the time dynamic is specified by random passage times attached to the edges. In this paper, the speed of the growth and the shape of the infected set is studied by aid of large-scale computer simulations, with focus on continuous passage time distributions. It is found that the most important quantity for determining the value of the time constant, which indicates the inverse asymptotic speed of the growth, is , where are i.i.d. passage time variables. The relation is linear for a large class of passage time distributions. Furthermore, the directional time constants are seen to be increasing when moving from the axis towards the diagonal, so that the limiting shape is contained in a circle with radius defined by the speed along the axes. The shape comes closer to the circle for distributions with larger variability.
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