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Sökning: WFRF:(Linusson Svante)

  • Resultat 1-10 av 68
  • [1]234567Nästa
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  • Alm, Sven Erick, et al. (författare)
  • Correlations for Paths in Random Orientations of G(n, p) and G(n, m)
  • 2011
  • Ingår i: ; 39:4, s. 486-506
  • 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.
  • Alm, Sven Erick, et al. (författare)
  • First critical probability for a problem on random orientations in G(n,p)
  • 2014
  • Ingår i: ; 19, s. 69-
  • 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.
  • Eriksson, Henrik, et al. (författare)
  • Dense packing of patterns in a permutation
  • 2007
  • Ingår i: Annals of Combinatorics. - 0218-0006 .- 0219-3094. ; 11:3-4, s. 459-470
  • Tidskriftsartikel (refereegranskat)abstract
    • We study the length L-k of the shortest permutation containing all patterns of length k. We establish the bounds e(-2)k(2) < L-k <= (2/3 + o(1))k(2). We also prove that as k there are permutations of length (1/4+o(1))k(2) containing almost all patterns of length k.
  • Janson, Svante, et al. (författare)
  • Proportionella val inom kommunfullmäktige
  • 2019
  • Rapport (övrigt vetenskapligt)abstract
    •  Vi diskuterar två olika problem som kan uppstå vid proportionella val i kommunfullmäktige och regionfullmäktige når ett parti försöker en kupp genom att utan samtycke gå i kartell med ett annat parti vid val till nämnd eller styrelse, vilket aktualiserades i åtminstone ett par fall hösten 2018. Det första problemet är vad sådana oönskade valkarteller kan få för effekter, och vilka möjligheter det finns för ett parti att skydda sig från att bli del i en oönskad valkartell. Det andra problemet är att i en sådan valkartell kan ett parti genom att splittra upp sina kandidater strategiskt  på flera olika valsedlar få fler platser i en nämnd är vad som är proportionellt. Detta andra problem bottnar i att lagen om proportionella val stipulerar att Thieles metod skall användas för fördelning inom kartellen. På detta problem finns en enkel matematisk lösning och vi argumenterar för att man skall byta till Phragméns metod som används för motsvarande val till utskott i riksdagen.
  • Janson, Svante, et al. (författare)
  • The Probability Of The Alabama Paradox
  • 2012
  • Ingår i: ; 49:3, s. 773-794
  • Tidskriftsartikel (refereegranskat)abstract
    • Hamilton's method is a natural and common method to distribute seats proportionally between states (or parties) in a parliament. In the USA it has been abandoned due to some drawbacks, in particular the possibility of the Alabama paradox, but it is still in use in many other countries. In this paper we give, under certain assumptions, a closed formula for the asymptotic probability, as the number of seats tends to infinity, that the Alabama paradox occurs given the vector p(l), ..., p(m) of relative sizes of the states. From the formula we deduce a number of consequences. For example, the expected number of states that will suffer from the Alabama paradox is asymptotically bounded above by 1/e and on average approximately 0.123.
  • Johansson, Robert, et al. (författare)
  • Pattern avoidance in alternating sign matrices
  • 2007
  • Ingår i: Annals of Combinatorics. - 0218-0006 .- 0219-3094. ; 11:04-mar, s. 471-480
  • Tidskriftsartikel (refereegranskat)abstract
    • We generalize the definition of a pattern from permutations to alternating sign matrices. The number of alternating sign matrices avoiding 132 is proved to be counted by the large Schroder numbers, 1, 2, 6, 22, 90, 394,.... We give a bijection between 132-avoiding alternating sign matrices and Schroder paths, which gives a refined enumeration. We also show that the 132-, 123-avoiding alternating sign matrices are counted by every second Fibonacci number.
  • Linusson, Svante, et al. (författare)
  • Completing a (k-1)-assignment
  • 2007
  • Ingår i: Combinatorics, probability & computing. - 0963-5483 .- 1469-2163. ; 16:4, s. 621-629
  • Tidskriftsartikel (refereegranskat)abstract
    • We consider the distribution of the value of the optimal k-assignment in an in x n matrix, where the entries are independent exponential random variables with arbitrary rates. We give closed formulas for both the Laplace transform of this random variable and for its expected value under the condition that there is a zero-cost (k - 1)-assignment.
  • Aas, Erik, 1990- (författare)
  • A Markov Process on Cyclic Words
  • 2014
  • Doktorsavhandling (övrigt vetenskapligt)abstract
    • The TASEP (totally asymmetric simple exclusion process) studied here is a Markov chain on cyclic words over the alphabet{1,2,...,n} given by at each time step sorting an adjacent pair of letters chosen uniformly at random. For example, from the word 3124 one may go to 1324, 3124, 3124, 4123 by sorting the pair 31, 12, 24, or 43.Two words have the sametype if they are permutations of each other. If we restrict TASEP to words of some particular type m we get an ergodic Markov chain whose stationary distribution we denote by ζm. Soζm (u) is the asymptotic proportion of time spent in the state u if the chain started in some word of type m. The distribution ζ is the main object of study in this thesis. This distribution turns out to have several remarkable properties, and alternative characterizations. It has previously been studied both from physical, combinatorial, and probabilitistic viewpoints.In the first chapter we give an extended summary of known results and results in this thesis concerning ζ. The new results are described (and proved) in detail in Papers I - IV.The new results in Papers I and II include an explicit formula for the value ofζat sorted words and a product formula for decomposable words. We also compute some correlation functions for ζ. In Paper III we study of a generalization of TASEP to Weyl groups. In Paper IV we study a certain scaling limit of ζ, finding several interesting patterns of which we prove some. We also study an inhomogenous version of TASEP, in which different particles get sorted at different rates, which generalizes the homogenous version in several aspects. In the first chapter we compute some correlation functions for ζ
  • Aas, Erik, et al. (författare)
  • Continuous multi-line queues and TASEP
  • 2018
  • Ingår i: ANNALES DE L INSTITUT HENRI POINCARE D. - : EUROPEAN MATHEMATICAL SOC. - 2308-5827. ; 5:1, s. 127-152
  • Tidskriftsartikel (refereegranskat)abstract
    • In this paper, we study a distribution Xi of labeled particles on a continuous ring. It arises in three different ways, all related to the multi-type TASEP on a ring. We prove formulas for the probability density function for some permutations and give conjectures for a larger class. We give a complete conjecture for the probability of two particles i, j being next to each other on the cycle, for which we prove some cases. We also find that two natural events associated to the process have exactly the same probability expressed as a Vandermonde determinant. It is unclear whether this is just a coincidence or a consequence of a deeper connection.
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