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  • 1
    Electronic Resource
    Electronic Resource
    Asymptotic behaviour of a Brownian motion on exterior domains (2000)
    Springer
    Probability theory and related fields 116 (2000), S. 303-316 
    Details
    ISSN: 1432-2064
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract. We study the asymptotic behaviour of the transition density of a Brownian motion in ?, killed at ∂?, where ? c is a compact non polar set. Our main result concern dimension d = 2, where we show that the transition density p ? t (x, y) behaves, for large t, as u(x)u(y)(t(log t)2)−1 for x, y∈?, where u is the unique positive harmonic function vanishing on (∂?) r , such that u(x) ∼ log ∣x∣.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s004400050251
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    The PMC processes associated to the (1/2, 1/2)-Bernoulli shift are also Bernoulli (1987)
    Springer
    Journal of statistical physics 47 (1987), S. 527-541 
    Details
    ISSN: 1572-9613
    Keywords: Markov processes ; Bernoulli shifts ; stable manifold ; strong convergence to equilibrium ; Nelson measure
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract It is proven that the Prigogine-Misra-Courbage (PMC) processes associated to the (1/2, 1/2)-Bernoulli shift are Bernoulli shifts. The Bernoulli partitions are constructed explicitly by using the decomposition of the transition kernels of the PMC processes on the fibers of the stable manifold of the transformed point (the generating property of these partitions is proved for any two-symbol Bernoulli shifts).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01007524
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    A lower bound for the memory capacity in the Potts-Hopfield model (1992)
    Springer
    Journal of statistical physics 66 (1992), S. 1643-1652 
    Details
    ISSN: 1572-9613
    Keywords: Neural network ; Hopfield model ; Potts model
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We consider Potts-Hopfield networks of sizeN. We prove the result: ∃α c 〉0 such that for all 0〈α〈α c we can findδ, ɛ〉0 in such a way that, whenN→∞, we can store αN patterns, all of them being sorrounded by ɛ-energy barriers at distanceδ.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01054440
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    The one-site distribution of Gibbs states on Bethe lattice are probability vectors of period⩽2 for a nonlinear transformation (1988)
    Springer
    Journal of statistical physics 52 (1988), S. 267-285 
    Details
    ISSN: 1572-9613
    Keywords: Gibbs states ; Bethe lattice ; spin vector ; dynamical systems ; automata networks ; subdifferential ; cyclically monotone function ; convex function ; Liapunov functional
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We prove that the one-site distribution of Gibbs states (for any finite spin setS) on the Bethe lattice is given by the points satisfying the equation π=T 2π, whereT=h·A·ϕ, withϕ(x)=x (q−1/q,h(x)=(x∥x∥ q ) q ,A=(a(r, s)∶r, s∈S), and $$a(r,s) = \exp (K[r,s] + (1/q)[N,r + s])$$ We also show that forA a symmetric, irreducible operator the nonlinear evolution on probability vectorsx(n+1)=Ax(n) p ∥Ax(n) p ∥1 withp〉0 has limit pointsξ of period⩽2. We show thatA positive definite implies limit points are fixed points that satisfy the equationAξ p=λξ. The main tool is the construction of a Liapunov functional by means of convex analysis techniques.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01016414
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  • 5
    Electronic Resource
    Electronic Resource
    Fluctuations in Derrida's random energy and generalized random energy models (1989)
    Springer
    Journal of statistical physics 54 (1989), S. 515-529 
    Details
    ISSN: 1572-9613
    Keywords: Random energy ; random variables ; finite-size corrections ; Poisson point process
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The fluctuations of the finite-size corrections to the free energy per site of the random energy model (REM) and the generalized random energy model (GREM) are investigated. Almost sure behavior for the corrections of order (logN)/N is given. We also prove convergence in distribution for the corrections of order 1/N.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01023492
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    Paper (German National Licenses)
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  • 6
    Electronic Resource
    Electronic Resource
    Erratum: The one-site distribution of Gibbs states on Bethe lattice are probability vectors of period ≤2 for a nonlinear transformation (1996)
    Springer
    Journal of statistical physics 82 (1996), S. 451-451 
    Details
    ISSN: 1572-9613
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02189240
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    Paper (German National Licenses)
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  • 7
    Electronic Resource
    Electronic Resource
    On Cesàro Limit Distribution of a Class of Permutative Cellular Automata (1998)
    Springer
    Journal of statistical physics 90 (1998), S. 435-452 
    Details
    ISSN: 1572-9613
    Keywords: Permutative cellular automata ; mod 2 automaton ; Cesàro means ; Bernoulli measures
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We study Cesàro means (time averages) of the evolution measures of the class of permutative cellular automata over {0, 1}ℕ defined by % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaiikaiabew% 9aQnaaBaaaleaacaWGcbaabeaakiaadIhacaGGPaWaaSbaaSqaaiaa% d6gaaeqaaOGaeyypa0JaamiEamaaBaaaleaacaWGUbGaaGjcVlaayI% W7cqGHRaWkcaaMi8UaaGjcVlaadkfaaeqaaOGaey4kaSIaeuiOda1a% a0baaSqaaiaadQgacaaMi8UaaGjcVlabg2da9iaayIW7caaMi8UaaG% imaaqaaiaadkfacaaMi8UaaGjcVlabgkHiTiaayIW7caaMi8UaaGym% aaaakiaayIW7caaMi8UaaGjcVlaayIW7caaMi8UaaGjcVlaacIcaca% aIXaGaey4kaSIaamOyamaaBaaaleaacaWGQbaabeaakiabgUcaRiaa% dIhadaWgaaWcbaGaamOBaiaayIW7caaMi8Uaey4kaSIaaGjcVlaayI% W7caWGQbaabeaakiaacMcaaaa!7530! $$(\varphi _B x)_n = x_{n{\kern 1pt} {\kern 1pt} + {\kern 1pt} {\kern 1pt} R} + \Pi _{j{\kern 1pt} {\kern 1pt} = {\kern 1pt} {\kern 1pt} 0}^{R{\kern 1pt} {\kern 1pt} - {\kern 1pt} {\kern 1pt} 1} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} (1 + b_j + x_{n{\kern 1pt} {\kern 1pt} + {\kern 1pt} {\kern 1pt} j} )$$ where B=b 0 ⋯ b R-1is an aperiodic block in {0, 1} R and operations are taken mod 2. If the initial measure is Bernoulli, we prove that the limit of the Cesàro mean of the first column distribution exists. When R = 1 and B = 1, φ B is the mod 2 sum automaton. For this automaton we show that the limit is the (1/2, 1/2(-Bernoulli measure, and if the initial measure is Markov, we show that the limit of Cesàro mean of the one-site distribution is equidistributed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1023276306998
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  • 8
    Electronic Resource
    Electronic Resource
    Truncated Pareto Law and Oresize Distribution of Ground Rocks (1998)
    Springer
    Mathematical geology 30 (1998), S. 661-673 
    Details
    ISSN: 1573-8868
    Keywords: self-similarity ; truncated exponential ; rock fragmentation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract We have studied the lower and upper truncated Pareto law. This distribution depends on three parameters, the upper and the lower bounds and a parameter m which measures whether the distribution concentrates on larger or smaller values of the variable. We have constructed a test for the null hypothesis H 0 :m = 1, which has a special significance from a theoretical point of view and also because in the samples that we consider, the estimation of m lies around 1. The truncated Pareto law is considered in the study of size frequency of rock fragmentation and we illustrate it with data corresponding to the ore size of rocks feeding an SAG mill at Chuquicamata mine in Chile. The data are the weights of the rocks for some classes defined by their mesh size and we propose an estimation method in its analysis.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1022391218233
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    Paper (German National Licenses)
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  • 9
    Online Resource
    Online Resource
    Quasi-Stationary Distributions : Markov Chains, Diffusions and Dynamical Systems (2013)
    Berlin :Springer-Verlag,
    Details
    Title: Quasi-Stationary Distributions : Markov Chains, Diffusions and Dynamical Systems
    Author: Collet, Pierre
    Contributer: Martinez, Servet , San Martin, Jaime
    Publisher: Berlin :Springer-Verlag,
    Year of publication: 2013
    ISBN: 978-3-642-33131-2
    Type of Medium: Online Resource
    Language: English
    URL: https://search.ebscohost.com/login.aspx?direct=true&db=nlebk&AN=528424&site=ehost-live
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    ZIB Catalog
    Zuse Institute Berlin
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