scholarly journals Harry Kesten’s work in probability theory

2021 ◽  
Author(s):  
Geoffrey R. Grimmett
Keyword(s):  
Probability Theory ◽  
Random Walks ◽  
Branching Processes

AbstractWe survey the published work of Harry Kesten in probability theory, with emphasis on his contributions to random walks, branching processes, percolation, and related topics.

RANDOM WALKS WITH HEAVY TAILS AND LIMIT THEOREMS FOR BRANCHING PROCESSES WITH MIGRATION AND IMMIGRATION

2012 ◽  
Vol 12 (01) ◽  
pp. 1150007 ◽  
Author(s):  
YAQIN FENG ◽  
STANISLAV MOLCHANOV ◽  
JOSEPH WHITMEYER
Keyword(s):  
Random Walks ◽  
Limit Theorems ◽  
Heavy Tails ◽  
Stochastic Dynamics ◽  
Branching Processes ◽  
Spatial Dynamics ◽  
Limiting Distributions ◽  
Central Result

The central result of this paper is the existence of limiting distributions for two classes of critical homogeneous-in-space branching processes with heavy tails spatial dynamics in dimension d = 2. In dimension d ≥ 3, the same results are true without any special assumptions on the underlying (non-degenerated) stochastic dynamics.

scholarly journals Measure-valued branching processes associated with random walks on $p$-adics

2000 ◽  
Vol 28 (4) ◽  
pp. 1680-1710 ◽  
Author(s):  
Sergio Albeverio ◽  
Xuelei Zhao
Keyword(s):  
Random Walks ◽  
Branching Processes

scholarly journals Recurrence and Transience of Critical Branching Processes in Random Environment with Immigration and an Application to Excited Random Walks

2014 ◽  
Vol 46 (03) ◽  
pp. 687-703 ◽  
Author(s):  
Elisabeth Bauernschubert
Keyword(s):  
Random Walk ◽  
Random Walks ◽  
Random Environment ◽  
Branching Processes ◽  
Random Environments ◽  
Recurrent Random Walk ◽  
The Right

We establish recurrence and transience criteria for critical branching processes in random environments with immigration. These results are then applied to the recurrence and transience of a recurrent random walk in a random environment on ℤ disturbed by cookies inducing a drift to the right of strength 1.

scholarly journals Positively and negatively excited random walks on integers, with branching processes

2008 ◽  
Vol 13 (0) ◽  
pp. 1952-1979 ◽  
Author(s):  
Elena Kosygina ◽  
Martin Zerner
Keyword(s):  
Random Walks ◽  
Branching Processes

scholarly journals The connection between evolution algebras, random walks and graphs

2019 ◽  
Vol 19 (02) ◽  
pp. 2050023 ◽  
Author(s):  
Paula Cadavid ◽  
Mary Luz Rodiño Montoya ◽  
Pablo M. Rodriguez
Keyword(s):  
Probability Theory ◽  
Markov Chain ◽  
Random Walk ◽  
Random Walks ◽  
Discrete Time ◽  
Associative Algebras ◽  
Biological Phenomena ◽  
Evolution Algebra ◽  
New Type ◽  
Markov Evolution

Evolution algebras are a new type of non-associative algebras which are inspired from biological phenomena. A special class of such algebras, called Markov evolution algebras, is strongly related to the theory of discrete time Markov chains. The winning of this relation is that many results coming from Probability Theory may be stated in the context of Abstract Algebra. In this paper, we explore the connection between evolution algebras, random walks and graphs. More precisely, we study the relationships between the evolution algebra induced by a random walk on a graph and the evolution algebra determined by the same graph. Given that any Markov chain may be seen as a random walk on a graph, we believe that our results may add a new landscape in the study of Markov evolution algebras.

Random Walks, Branching Processes

2019 ◽  
pp. 45-51
Author(s):  
Alan Weiss ◽  
Adam Shwartz
Keyword(s):  
Random Walks ◽  
Branching Processes

A BOUNDED VARIATION ESTIMATE FOR THE FORCE SCHEME APPLIED TO STRICTLY HYPERBOLIC SYSTEMS OF CONSERVATION LAWS IN THE TEMPLE CLASS

2013 ◽  
Vol 10 (01) ◽  
pp. 105-127
Author(s):  
RAJIB DUTTA
Keyword(s):  
Probability Theory ◽  
Initial Data ◽  
Conservation Laws ◽  
Random Walks ◽  
Total Variation ◽  
Bounded Variation ◽  
Hyperbolic Systems ◽  
Godunov Scheme ◽  
Systems Of Conservation Laws ◽  
The Temple

Bressan and Jenssen established a uniform bounded variation (BV) estimate for the Godunov scheme for Temple-type strictly hyperbolic systems of conservation laws and gave a proof based on the probability theory of random walks. In this paper, we provide a different proof which is simpler and does not use any probability theory. Applying our theory, we establish a uniform BV estimate for the Force scheme for the same class of hyperbolic systems, under the assumption of small total variation of initial data.

scholarly journals An Almost-Sure Renewal Theorem for Branching Random Walks on the Line

2010 ◽  
Vol 47 (03) ◽  
pp. 811-825
Author(s):  
Matthias Meiners
Keyword(s):  
Random Walks ◽  
Real Line ◽  
Branching Processes ◽  
Almost Sure Convergence ◽  
General Characteristic ◽  
Renewal Theorem ◽  
The Real ◽  
Branching Random Walks

In the present paper an almost-sure renewal theorem for branching random walks (BRWs) on the real line is formulated and established. The theorem constitutes a generalization of Nerman's theorem on the almost-sure convergence of Malthus normed supercritical Crump-Mode-Jagers branching processes counted with general characteristic and Gatouras' almost-sure renewal theorem for BRWs on a lattice.

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