Karl Grill
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Research Subjects
Karl Grill has a total of 7 co-authors. Here are the top co-authors by number of shared publications:
- Christian Tutschka
Institut für Theoretische Physik, TU Wien
2 shared publications - Zsolt Saffer
Department of Information Systems Engineering and Management, The Distance-Learning University of Applied Sciences (FERNFH), Wiener Neustadt, Austria;Institute of Statistics and Mathematical Methods in Economics, Vienna University of Technology, Vienna, Austria
2 shared publications - Christian Tutschka
Erwin Schrödinger Institute for Mathematical Physics, Boltzmanngasse 9, 1090 Wien, Austria
1 shared publication - Daniel Linzmayer1 shared publication
Endre Csáki
Mathematical Institute of the Hungarian Academy of Sciences, Reàltanoda U. 13-15, 1053 Budapest, Hungary
1 shared publication- Miklós Telek
Budapest University of Technology and Economics
1 shared publication
Latest Publications
- 28 May 2026
- Published by Springer Nature
- p. 173-181
An Overview of Property B
- Open Access
An Erdős-Révész Type Law for the Length of the Longest Match of Two Coin-Tossing Sequences
Consider a coin-tossing sequence, i.e., a sequence of independent variables, taking values 0 and 1 with probability . The famous Erdős-Rényi law of large numbers implies that the longest run of ones in the first n observations has a length that behaves like , as n tends to infinity (throughout this article, log denotes logarithm with base 2). Erdős and Révész refined this result by providing a description of the Lévy upper and lower classes of the process . In another direction, Arratia and Waterman extended the Erdős-Rényi result to the longest matching subsequence (with shifts) of two coin-tossing sequences, finding that it behaves asymptotically like . The present paper provides some Erdős-Révész type results in this situation, obtaining a complete description of the upper classes and a partial result on the lower ones.Open AccessAn Erdős-Révész Type Law for the Length of the Longest Match of Two Coin-Tossing Sequences
Consider a coin-tossing sequence, i.e., a sequence of independent variables, taking values 0 and 1 with probability . The famous Erdős-Rényi law of large numbers implies that the longest run of ones in the first n observations has a length that behaves like , as n tends to infinity (throughout this article, log denotes logarithm with base 2). Erdős and Révész refined this result by providing a description of the Lévy upper and lower classes of the process . In another direction, Arratia and Waterman extended the Erdős-Rényi result to the longest matching subsequence (with shifts) of two coin-tossing sequences, finding that it behaves asymptotically like . The present paper provides some Erdős-Révész type results in this situation, obtaining a complete description of the upper classes and a partial result on the lower ones. - Open Access
- 18 November 2024
- Published by MDPI AG in Preprints.org
An Erdős-Révész Type Law for the Length of the Longest Match of Two Coin-Tossing Sequences
Consider a coin-tossing sequence, i.e., a sequence of independent variables taking values 0 and 1 with probability 1/2. The famous Erdős-Rényi (1970) law of large numbers implies that the longest run of ones in the first n observations has a length Rn that behaves like log2(n) as n tends to infinity. Erdős and Révész (1976) refined this result by giving a description of the Lévy upper and lower classes of the process Rn. In another direction, Arratia and Waterman (1985) extended the Erdős-Rényi result to the longest matching subsequence (with shifts) of two coin-tossing sequences, finding that it behaves asymptotically like 2log2(n). The present paper gives some Erdős-Révész-type results in this situation, obtaining a complete description of the upper classes and a partial result on the lower ones.
- 18 November 2024
- Published by MDPI AG in Preprints.org
Open AccessAn Erdős-Révész Type Law for the Length of the Longest Match of Two Coin-Tossing Sequences
Consider a coin-tossing sequence, i.e., a sequence of independent variables taking values 0 and 1 with probability 1/2. The famous Erdős-Rényi (1970) law of large numbers implies that the longest run of ones in the first n observations has a length Rn that behaves like log2(n) as n tends to infinity. Erdős and Révész (1976) refined this result by giving a description of the Lévy upper and lower classes of the process Rn. In another direction, Arratia and Waterman (1985) extended the Erdős-Rényi result to the longest matching subsequence (with shifts) of two coin-tossing sequences, finding that it behaves asymptotically like 2log2(n). The present paper gives some Erdős-Révész-type results in this situation, obtaining a complete description of the upper classes and a partial result on the lower ones.
- 7 October 2023
- Published by Springer Nature
- p. 81-95
M/G/1 Queue with State Dependent Service Times
- 10 June 2018
- Published by Springer Nature
- p. 51-63
Controllable Capacity Queue with Synchronous Constant Service Time and Loss
- 10 June 2018
- Published by Springer Nature
- p. 51-63
Controllable Capacity Queue with Synchronous Constant Service Time and Loss
- Open Access
- 1 January 2015
- Published by American Institute of Mathematical Sciences (AIMS) in Discrete and Continuous Dynamical Systems
- Vol. 35 (10) , 4831-4838
Ergodicity of two particles with attractive interaction
We study the ergodic properties of a classical two-particle system with square-well pair potential in an interval.
- 1 January 2015
- Published by American Institute of Mathematical Sciences (AIMS) in Discrete and Continuous Dynamical Systems
- Vol. 35 (10) , 4831-4838
Open AccessErgodicity of two particles with attractive interaction
We study the ergodic properties of a classical two-particle system with square-well pair potential in an interval.
- 6 October 2006
- Published by Springer Nature in Journal of Statistical Physics
- Vol. 125 (3) , 717-726
Lattice Gas with Finite-Range Interaction Under Gravity
- 6 October 2006
- Published by Springer Nature in Journal of Statistical Physics
- Vol. 125 (3) , 717-726
Lattice Gas with Finite-Range Interaction Under Gravity
- 1 December 2004
- Published by Springer Nature in Journal of Statistical Physics
- Vol. 117 (5-6) , 1015-1022
One-Dimensional Falling Bodies
- 1 December 2004
- Published by Springer Nature in Journal of Statistical Physics
- Vol. 117 (5-6) , 1015-1022
One-Dimensional Falling Bodies
- 1 October 1997
- Published by Elsevier in Stochastic Processes and their Applications
- Vol. 71 (1) , 1-10
Strassen-type laws for independent random walks
- 1 October 1997
- Published by Elsevier in Stochastic Processes and their Applications
- Vol. 71 (1) , 1-10
Strassen-type laws for independent random walks
- 1 February 1996
- Published by Elsevier in Statistics & Probability Letters
- Vol. 26 (3) , 213-218
The range of simple branching random walk
- 1 February 1996
- Published by Elsevier in Statistics & Probability Letters
- Vol. 26 (3) , 213-218
The range of simple branching random walk