The Experts below are selected from a list of 15579 Experts worldwide ranked by ideXlab platform
R. Straka - One of the best experts on this subject based on the ideXlab platform.
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Solutions of evolution equations for medium-induced QCD cascades
The European Physical Journal C, 2019Co-Authors: K. Kutak, W. Płaczek, R. StrakaAbstract:In this paper we present solutions of evolution equations for inclusive distribution of gluons as produced by jet traversing quark–gluon plasma. We reformulate the original equations in such a form that virtual and unresolved-real emissions as well as unresolved collisions with medium are resummed in a Sudakov-type form factor. The resulting integral equations are then solved most efficiently with use of newly developed Markov Chain Monte Carlo algorithms implemented in a dedicated program called MINCAS . Their results for a gluon energy density are compared with an analytical solution and a differential numerical method. Some results for gluon transverse-momentum distributions are also presented. They exhibit interesting patterns not discussed so far in the literature, in particular a departure from the Gaussian Behaviour – which does not happen in approximate analytical solutions.
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Solutions of evolution equations for medium-induced QCD cascades
The European Physical Journal C, 2019Co-Authors: K. Kutak, Wieslaw Placzek, R. StrakaAbstract:In this paper we present solutions of evolution equations for inclusive distribution of gluons as produced by jet traversing quark-gluon plasma. We reformulate the original equations in such a form that the virtual and unresolved-real emissions as well as unresolved collisions with medium are resummed in a Sudakov-type form factor. The resulting integral equations are then solved most efficiently with use of newly developed Markov Chain Monte Carlo algorithms implemented in a dedicated program called MINCAS. Their results for a gluon energy density are compared with an analytical solution and a differential numerical method. Some results for gluon transverse-momentum distributions are also presented. They exhibit interesting patterns not discussed so far in the literature, in particular a departure from the Gaussian Behaviour - which does not happen in approximate analytical solutions.
Gordon Slade - One of the best experts on this subject based on the ideXlab platform.
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High-dimensional graphical networks of self-avoiding walks
Canadian Journal of Mathematics, 2004Co-Authors: Mark Holmes, Antal A. Járai, Akira Sakai, Gordon SladeAbstract:We use the lace expansion to analyse networks of mutually-avoiding self-avoiding walks, having the topology of a graph. The networks are defined in terms of spread-out self-avoiding walks that are permitted to take large steps. We study the asymptotic Behaviour of networks in the limit of widely separated network branch points, and prove Gaussian Behaviour for sufficiently spread-out networks on ${{\mathbb{Z}}^{d}}$ in dimensions $d\,>\,4$ .
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The lace expansion on a tree with application to networks of self-avoiding walks
Advances in Applied Mathematics, 2003Co-Authors: Remco Van Der Hofstad, Gordon SladeAbstract:The lace expansion has been used successfully to study the critical Behaviour in high dimensions of self-avoiding walks, lattice trees and lattice animals, and percolation. In each case, the lace expansion has been an expansion along a time interval. In this paper, we introduce the lace expansion on a tree, in which 'time' is generalised from an interval to a tree. We develop the expansion in the context of networks of mutually-avoiding self-avoiding walks joined together with the topology of a tree, in dimensions d>4, and prove Gaussian Behaviour for sufficiently spread-out networks consisting of long self-avoiding walks.
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Convergence of critical oriented percolation to super-Brownian motion above 4+1 dimensions
Annales de l?Institut Henri Poincare (B) Probability and Statistics, 2003Co-Authors: Remco Van Der Hofstad, Gordon SladeAbstract:Abstract We consider oriented bond percolation on Z d × N , at the critical occupation density pc, for d>4. The model is a “spread-out” model having long range parameterised by L. We consider configurations in which the cluster of the origin survives to time n, and scale space by n1/2. We prove that for L sufficiently large all the moment measures converge, as n→∞, to those of the canonical measure of super-Brownian motion. This extends a previous result of Nguyen and Yang, who proved Gaussian Behaviour for the critical two-point function, to all r-point functions (r⩾2). We use lace expansion methods for the two-point function, and prove convergence of the expansion using a general inductive method that we developed in a previous paper. For the r-point functions with r⩾3, we use a new expansion method.
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A new inductive approach to the lace expansion for self-avoiding walks
Probability Theory and Related Fields, 1998Co-Authors: Remco Van Der Hofstad, Frank Den Hollander, Gordon SladeAbstract:We introduce a new inductive approach to the lace expansion, and apply it to prove Gaussian Behaviour for the weakly self-avoiding walk on ℤ d where loops of length m are penalised by a factor e −β/m p (0 4, p≥0; (2) d≤4, . In particular, we derive results first obtained by Brydges and Spencer (and revisited by other authors) for the case d>4, p=0. In addition, we prove a local central limit theorem, with the exception of the case d>4, p=0.
Alex Grant - One of the best experts on this subject based on the ideXlab platform.
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non Gaussian Behaviour of extrinsic log values
International Symposium on Information Theory, 2004Co-Authors: Nick Letzepis, Alex GrantAbstract:The nonGaussian Behaviour of extrinsic log-values (L-values) during iterative turbo-decoding process is investigated in this paper. We assess the use of the Pearson system to model the extrinsic L-values nonGaussian Behaviour
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ISIT - Non-Gaussian Behaviour of extrinsic log-values
International Symposium onInformation Theory 2004. ISIT 2004. Proceedings., 1Co-Authors: Nick Letzepis, Alex GrantAbstract:The nonGaussian Behaviour of extrinsic log-values (L-values) during iterative turbo-decoding process is investigated in this paper. We assess the use of the Pearson system to model the extrinsic L-values nonGaussian Behaviour
K. Kutak - One of the best experts on this subject based on the ideXlab platform.
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Solutions of evolution equations for medium-induced QCD cascades
The European Physical Journal C, 2019Co-Authors: K. Kutak, W. Płaczek, R. StrakaAbstract:In this paper we present solutions of evolution equations for inclusive distribution of gluons as produced by jet traversing quark–gluon plasma. We reformulate the original equations in such a form that virtual and unresolved-real emissions as well as unresolved collisions with medium are resummed in a Sudakov-type form factor. The resulting integral equations are then solved most efficiently with use of newly developed Markov Chain Monte Carlo algorithms implemented in a dedicated program called MINCAS . Their results for a gluon energy density are compared with an analytical solution and a differential numerical method. Some results for gluon transverse-momentum distributions are also presented. They exhibit interesting patterns not discussed so far in the literature, in particular a departure from the Gaussian Behaviour – which does not happen in approximate analytical solutions.
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Solutions of evolution equations for medium-induced QCD cascades
The European Physical Journal C, 2019Co-Authors: K. Kutak, Wieslaw Placzek, R. StrakaAbstract:In this paper we present solutions of evolution equations for inclusive distribution of gluons as produced by jet traversing quark-gluon plasma. We reformulate the original equations in such a form that the virtual and unresolved-real emissions as well as unresolved collisions with medium are resummed in a Sudakov-type form factor. The resulting integral equations are then solved most efficiently with use of newly developed Markov Chain Monte Carlo algorithms implemented in a dedicated program called MINCAS. Their results for a gluon energy density are compared with an analytical solution and a differential numerical method. Some results for gluon transverse-momentum distributions are also presented. They exhibit interesting patterns not discussed so far in the literature, in particular a departure from the Gaussian Behaviour - which does not happen in approximate analytical solutions.
Sary Drappeau - One of the best experts on this subject based on the ideXlab platform.
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Limit laws for rational continued fractions and value distribution of quantum modular forms
2020Co-Authors: Sandro Bettin, Sary DrappeauAbstract:We study the limiting distributions of Birkhoff sums of a large class of cost functions (observables) evaluated along orbits, under the Gauss map, of rational numbers in~$(0,1]$ ordered by denominators. We show convergence to a stable law in a general setting, by proving an estimate with power-saving error term for the associated characteristic function. This extends results of Baladi and Vallée on Gaussian Behaviour for costs of moderate growth. We apply our result to obtain the limiting distribution of values of several key examples of quantum modular forms. We obtain the Gaussian Behaviour of central values of the Esterman function~$\sum_{n\geq 1} \tau(n) \e^{2\pi i n x}/\sqrt{n}$ ($x\in \Q$), a problem for which known approaches based on Eisenstein series have been so far ineffective. We give a new proof, based on dynamical systems, that central modular symbols associated with a holomorphic cusp form for~$SL(2,\Z)$ have a Gaussian distribution, and give the first proof of an estimate for their probabilities of large deviations. We also recover a result of Vardi on the convergence of Dedekind sums to a Cauchy law, using dynamical methods.
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Limit laws for rational continued fractions and value distribution of quantum modular forms
arXiv: Number Theory, 2020Co-Authors: Sandro Bettin, Sary DrappeauAbstract:We study the limiting distributions of Birkhoff sums of a large class of cost functions (observables) evaluated along orbits, under the Gauss map, of rational numbers in~$(0,1]$ ordered by denominators. We show convergence to a stable law in a general setting, by proving an estimate with power-saving error term for the associated characteristic function. This extends results of Baladi and Vallee on Gaussian Behaviour for costs of moderate growth. We apply our result to obtain the limiting distribution of values of several key examples of quantum modular forms. We obtain the Gaussian Behaviour of central values of the Esterman function~$\sum_{n\geq 1} \tau(n) \e^{2\pi i n x}/\sqrt{n}$ ($x\in \Q$), a problem for which known approaches based on Eisenstein series have been so far ineffective. We give a new proof, based on dynamical systems, that central modular symbols associated with a holomorphic cusp form for~$SL(2,\Z)$ have a Gaussian distribution, and give the first proof of an estimate for their probabilities of large deviations. We also recover a result of Vardi on the convergence of Dedekind sums to a Cauchy law, using dynamical methods.