Sven Erick Alm
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Research Subjects
Sven Erick Alm has a total of 7 co-authors. Here are the top co-authors by number of shared publications:
- Svante Linusson
Department of Mathematics, KTH-Royal Institute of Technology, SE-100 44, Stockholm, Sweden
5 shared publications - Maria Deijfen
Stockholm University
2 shared publications - Svante Janson
Uppsala University
2 shared publications - Gregory B. Sorkin
Department of Mathematics The London School of Economics and Political Science London UK
1 shared publication - John C. Wierman
Johns Hopkins University
1 shared publication - Robert Parviainen
Dept. of Mathematics, Uppsala University, PO Box 480, S-75106 Uppsala, Sweden
1 shared publication
Latest Publications
- 30 August 2015
- Published by Springer Nature in Journal of Statistical Physics
- Vol. 161 (3) , 657-678
First Passage Percolation on $\mathbb {Z}^2$ Z 2 : A Simulation Study- 30 August 2015
- Published by Springer Nature in Journal of Statistical Physics
- Vol. 161 (3) , 657-678
First Passage Percolation on $\mathbb {Z}^2$ Z 2 : A Simulation Study- Open AccessFirst passage percolation on $\mathbb{Z}^2$ -- a simulation studyFirst passage percolation on $\mathbb{Z}^2$ 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 $\mathbf{E}[\min\{\tau_1,\ldots,\tau_4\}]$, where $\tau_1,\ldots,\tau_4$ 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.Open AccessFirst passage percolation on $\mathbb{Z}^2$ -- a simulation studyFirst passage percolation on $\mathbb{Z}^2$ 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 $\mathbf{E}[\min\{\tau_1,\ldots,\tau_4\}]$, where $\tau_1,\ldots,\tau_4$ 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.
- Open AccessFirst critical probability for a problem on random orientations in $G(n,p)$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 $a \to s$ and $s\to b$. We prove that asymptotically the correlation is negative for small $p$, $p<\frac{C_1}n$, where $C_1\approx0.3617$, positive for $\frac{C_1}n<p<\frac2n$ and up to $p=p_2(n)$. Computer aided computations suggest that $p_2(n)=\frac{C_2}n$, with $C_2\approx7.5$. We conjecture that the correlation then stays negative for $p$ up to the previously known zero at $\frac12$; for larger $p$ it is positive.Open AccessFirst critical probability for a problem on random orientations in $G(n,p)$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 $a \to s$ and $s\to b$. We prove that asymptotically the correlation is negative for small $p$, $p<\frac{C_1}n$, where $C_1\approx0.3617$, positive for $\frac{C_1}n<p<\frac2n$ and up to $p=p_2(n)$. Computer aided computations suggest that $p_2(n)=\frac{C_2}n$, with $C_2\approx7.5$. We conjecture that the correlation then stays negative for $p$ up to the previously known zero at $\frac12$; for larger $p$ it is positive.
- 15 March 2011
- Published by Wiley in Random Structures & Algorithms
- Vol. 39 (4) , 486-506
Correlations for paths in random orientations of G(n,p) and G(n,m)
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 combine probability space, of the events $\{a\to s\}$ and $\{s\to b\}$ .For G(n,p), we prove that there is a $pc = 1/2$ such that for a fixed $p < pc$ the correlation is negative for large enough n and for $p > pc$ the correlation is positive for large enough n. We conjecture that for a fixed $n \ge 27$ the correlation changes sign three times for three critical values of p.For G(n,m) it is similarly proved that, with $p=m/({{n}\atop {2}})$ , there is a critical pc 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 $\ell$ directed edges in G(n,m), is thought to be of independent interest.We present exact recursions to compute \input amssym $\Bbb{P}(a\to s)$ and \input amssym $\Bbb{P}(a\to s, s\to b)$. We also briefly discuss the corresponding question in the quenched version of the problem. © 2011 Wiley Periodicals, Inc. Random Struct. Alg., 2011- 15 March 2011
- Published by Wiley in Random Structures & Algorithms
- Vol. 39 (4) , 486-506
Correlations for paths in random orientations of G(n,p) and G(n,m)
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 combine probability space, of the events $\{a\to s\}$ and $\{s\to b\}$ .For G(n,p), we prove that there is a $pc = 1/2$ such that for a fixed $p < pc$ the correlation is negative for large enough n and for $p > pc$ the correlation is positive for large enough n. We conjecture that for a fixed $n \ge 27$ the correlation changes sign three times for three critical values of p.For G(n,m) it is similarly proved that, with $p=m/({{n}\atop {2}})$ , there is a critical pc 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 $\ell$ directed edges in G(n,m), is thought to be of independent interest.We present exact recursions to compute \input amssym $\Bbb{P}(a\to s)$ and \input amssym $\Bbb{P}(a\to s, s\to b)$. We also briefly discuss the corresponding question in the quenched version of the problem. © 2011 Wiley Periodicals, Inc. Random Struct. Alg., 2011- Open Access
Correlations for paths in random orientations of G(n,p) and G(n,m)
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 pp_c the correlation is positive for large enough n. We conjecture that for a fixed n\ge 27 the correlation changes sign three times for three critical values of p. For G(n,m) it is similarly proved that, with $p=m/\binom{n}{2}$, 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 k 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.Open AccessCorrelations for paths in random orientations of G(n,p) and G(n,m)
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 pp_c the correlation is positive for large enough n. We conjecture that for a fixed n\ge 27 the correlation changes sign three times for three critical values of p. For G(n,m) it is similarly proved that, with $p=m/\binom{n}{2}$, 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 k 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. - 13 May 2010
- Published by Cambridge University Press (CUP) in Combinatorics, Probability and Computing
- Vol. 20 (1) , 1-9
A Counter-Intuitive Correlation in a Random Tournament
Consider a randomly oriented graphG= (V, E) and leta,sandbbe three distinct vertices inV. We study the correlation between the events {a→s} and {s→b}. We show that, counter-intuitively, whenGis the complete graphKn,n≥ 5, then the correlation is positive. (It is negative forn= 3 and zero forn= 4.) We briefly discuss and pose problems for the same question on other graphs.
- 13 May 2010
- Published by Cambridge University Press (CUP) in Combinatorics, Probability and Computing
- Vol. 20 (1) , 1-9
A Counter-Intuitive Correlation in a Random Tournament
Consider a randomly oriented graphG= (V, E) and leta,sandbbe three distinct vertices inV. We study the correlation between the events {a→s} and {s→b}. We show that, counter-intuitively, whenGis the complete graphKn,n≥ 5, then the correlation is positive. (It is negative forn= 3 and zero forn= 4.) We briefly discuss and pose problems for the same question on other graphs.
- Open Access
A counter-intuitive correlation in a random tournament
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 $\{a\to s\}$ and $\{s\to b\}$. We show that, when $G$ is the complete graph $K_n$, the correlation is negative for $n=3$, zero for $n=4$, and that, counter-intuitively, it is positive for $n\ge 5$. We also show that the correlation is always negative when $G$ is a cycle, $C_n$, and negative or zero when $G$ is a tree (or a forest).Open AccessA counter-intuitive correlation in a random tournament
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 $\{a\to s\}$ and $\{s\to b\}$. We show that, when $G$ is the complete graph $K_n$, the correlation is negative for $n=3$, zero for $n=4$, and that, counter-intuitively, it is positive for $n\ge 5$. We also show that the correlation is always negative when $G$ is a cycle, $C_n$, and negative or zero when $G$ is a tree (or a forest). - 7 June 2006
- Published by Cambridge University Press (CUP) in Combinatorics, Probability and Computing
- Vol. 15 (4) , 477-488
On Measures of Average Degree for Lattices
The usual definition of average degree for a non-regular lattice has the disadvantage that it takes the same value for many lattices with clearly different connectivity. We introduce an alternative definition of average degree, which better separates different lattices.These measures are compared on a class of lattices and are analysed using a Markov chain describing a random walk on the lattice. Using the new measure, we conjecture the order of both the critical probabilities for bond percolation and the connective constants for self-avoiding walks on these lattices.
- 7 June 2006
- Published by Cambridge University Press (CUP) in Combinatorics, Probability and Computing
- Vol. 15 (4) , 477-488
On Measures of Average Degree for Lattices
The usual definition of average degree for a non-regular lattice has the disadvantage that it takes the same value for many lattices with clearly different connectivity. We introduce an alternative definition of average degree, which better separates different lattices.These measures are compared on a class of lattices and are analysed using a Markov chain describing a random walk on the lattice. Using the new measure, we conjecture the order of both the critical probabilities for bond percolation and the connective constants for self-avoiding walks on these lattices.
- 1 September 2002
- Published by Cambridge University Press (CUP) in Combinatorics, Probability and Computing
- Vol. 11 (5) , 433-445
Lower and Upper Bounds for the Time Constant of First-Passage Percolation
We present improved lower and upper bounds for the time constant of first-passage percolation on the square lattice. For the case of lower bounds, a new method, using the idea of a transition matrix, has been used. Numerical results for the exponential and uniform distributions are presented. A simulation study is included, which results in new estimates and improved upper confidence limits for the time constants.
- 1 September 2002
- Published by Cambridge University Press (CUP) in Combinatorics, Probability and Computing
- Vol. 11 (5) , 433-445
Lower and Upper Bounds for the Time Constant of First-Passage Percolation
We present improved lower and upper bounds for the time constant of first-passage percolation on the square lattice. For the case of lower bounds, a new method, using the idea of a transition matrix, has been used. Numerical results for the exponential and uniform distributions are presented. A simulation study is included, which results in new estimates and improved upper confidence limits for the time constants.
- 1 May 2002
- Published by Cambridge University Press (CUP) in Combinatorics, Probability and Computing
- Vol. 11 (3) , 217-248
Exact Expectations and Distributions for the Random Assignment Problem
A generalization of the random assignment problem asks the expected cost of the minimum-cost matching of cardinality k in a complete bipartite graph Km,n, with independent random edge weights. With weights drawn from the exponential distribution with intensity 1, the answer has been conjectured to beΣi,j≥0, i+j<k1/(m−i)(n−j).Here, we prove the conjecture for k [les ] 4, k = m = 5, and k = m = n = 6, using a structured, automated proof technique that results in proofs with relatively few cases. The method yields not only the minimum assignment cost's expectation but the Laplace transform of its distribution as well. From the Laplace transform we compute the variance in these cases, and conjecture that, with k = m = n → ∞, the variance is 2/n + O(log n/n2). We also include some asymptotic properties of the expectation and variance when k is fixed.
- 1 May 2002
- Published by Cambridge University Press (CUP) in Combinatorics, Probability and Computing
- Vol. 11 (3) , 217-248
Exact Expectations and Distributions for the Random Assignment Problem
A generalization of the random assignment problem asks the expected cost of the minimum-cost matching of cardinality k in a complete bipartite graph Km,n, with independent random edge weights. With weights drawn from the exponential distribution with intensity 1, the answer has been conjectured to beΣi,j≥0, i+j<k1/(m−i)(n−j).Here, we prove the conjecture for k [les ] 4, k = m = 5, and k = m = n = 6, using a structured, automated proof technique that results in proofs with relatively few cases. The method yields not only the minimum assignment cost's expectation but the Laplace transform of its distribution as well. From the Laplace transform we compute the variance in these cases, and conjecture that, with k = m = n → ∞, the variance is 2/n + O(log n/n2). We also include some asymptotic properties of the expectation and variance when k is fixed.