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The Clairvoyant Demon Has a Hard Task [article]

Peter Gacs
2003 arXiv   pre-print
We say that this random configuration percolates if there is a path in L starting at the origin, consisting of rightward and upward unit steps, and avoiding the blocked points.  ...  A point of L will be called blocked if its row and column have the same color.  ...  both infinite sequences X and Y , can introduce delays into these walks in such a way that they never collide. 1.2.  ... 
arXiv:math/0302059v1 fatcat:yvy2rfcygngtbg7tsp3xtpwyse

The Clairvoyant Demon Has a Hard Task

PETER GÁCS
2000 Combinatorics, probability & computing  
We say that this random configuration percolates if there is a path in L starting at the origin, consisting of rightward and upward unit steps, and avoiding the blocked points.  ...  A point of L will be called blocked if its row and column have the same color.  ...  X and Y, can introduce delays into these walks in such a way that they never collide.  ... 
doi:10.1017/s0963548300004405 fatcat:mgxy6zozwzcj3ktayhy7c2zpty

Collisions of random walks in reversible random graphs

Tom Hutchcroft, Yuval Peres
2015 Electronic Communications in Probability  
We prove that in any recurrent reversible random rooted graph, two independent simple random walks started at the same vertex collide infinitely often almost surely.  ...  This applies to the Uniform Infinite Planar Triangulation and Quadrangulation and to the Incipient Infinite Cluster in Z^2.  ...  We thank Itai Benjamini for suggesting this problem, and also thank Lewis Bowen, Perla Sousi and Omer Tamuz for helpful discussions.  ... 
doi:10.1214/ecp.v20-4330 fatcat:mjs3rq24gvgy3ez3lu63p3eojy

Formation, Interaction and Observation of Topological Defects [article]

Tanmay Vachaspati
1999 arXiv   pre-print
In these lectures, I describe the formation of defect distributions in first-order phase transitions, then briefly discuss the relevance of defect interactions after a phase transition and the observational  ...  It is known that random walks do not close in 3 dimensions and this tells us that infinite strings will be present.  ...  The effect of including these factors on the random bubble lattice and percolation has not yet been studied.  ... 
arXiv:astro-ph/9903362v1 fatcat:es6k65yswrfphiwoyhpmt465zy

Formation, Interaction and Observation of Topological Defects [chapter]

Tanmay Vachaspati
2000 Topological Defects and the Non-Equilibrium Dynamics of Symmetry Breaking Phase Transitions  
In these lectures, I describe the formation of defect distributions in first-order phase transitions, then briefly discuss the relevance of defect interactions after a phase transition and the observational  ...  It is known that random walks do not close in 3 dimensions and this tells us that infinite strings will be present.  ...  The effect of including these factors on the random bubble lattice and percolation has not yet been studied.  ... 
doi:10.1007/978-94-011-4106-2_4 fatcat:cz6d2vnnsvcrbcz2p7q7emctt4

Polymer pinning in a random medium as influence percolation [chapter]

V. Beffara, V. Sidoravicius, H. Spohn, M. E. Vares
2006 Institute of Mathematical Statistics Lecture Notes - Monograph Series  
Differing from standard methods and techniques, we transform the problem to a particular dependent percolative system and relate the pinning transition to a percolation transition.  ...  Kesten and D. Surgailis for many hours of fruitful and clarifying discussions scattered over the past four years. We also thank CBPF, IMPA, TU-München for hospitality and financial support.  ...  Regular particles, starting from the points of ω n , are annihilated as soon as they collide with any other particle; Polymer pinning in a random medium as influence percolation 9 2.  ... 
doi:10.1214/074921706000000022 fatcat:hczxq4i6krbdtjcswnaozg24ya

Page 1949 of Mathematical Reviews Vol. , Issue 84e [page]

1984 Mathematical Reviews  
All particles perform independent simple symmetric random walks in continuous time at rate 1, except that whenever an X particle and a Y particle collide, they are both annihilated.  ...  Kesten on directed random walks on Z*. The lower bound results from coupling comparisons with branching processes and involves considerable computation.  ... 

Polymer pinning in a random medium as influence percolation [chapter]

V. Beffara, V. Sidoravicius, H. Spohn, M. E. Vares
2006 Lecture Notes-Monograph Series  
Differing from standard methods and techniques, we transform the problem to a particular dependent percolative system and relate the pinning transition to a percolation transition.  ...  Kesten and D. Surgailis for many hours of fruitful and clarifying discussions scattered over the past four years. We also thank CBPF, IMPA, TU-München for hospitality and financial support.  ...  Regular particles, starting from the points of ω n , are annihilated as soon as they collide with any other particle; Polymer pinning in a random medium as influence percolation 9 2.  ... 
doi:10.1214/lnms/1196285803 fatcat:il5jv2ohgfb35opgp4yx36ngtm

Application of fractal concepts to polymer statistics and to anomalous transport in randomly porous media

H. Eugene Stanley
1984 Journal of statistical physics  
a random walk on (a) a Euclidean lattice, and (b) a percolation cluster at the percolation threshold.the same time.  ...  Now the fractal dimension of a random walk is defined by imagining that the random walk is a free flight polymer chain (with no "excluded volume").  ... 
doi:10.1007/bf01012944 fatcat:lojeoc4bsbgjrag56ggs6sjhq4

Limiting distribution of last passage percolation models

JINHO BAIK
2006 XIVth International Congress on Mathematical Physics  
We survey some results and applications of last percolation models of which the limiting distribution can be evaluated.  ...  Acknowledgments The author would like to thank Percy Deift and Michio Jimbo for kindly inviting him to the special session of integrable systems in the International Congress on Mathematical Physics.  ...  Random vicious walks The combinatorics of the longest increasing subsequence and the Plancherel measure have an interpretation as non-intersecting paths, which is sometimes called vicious walks 20 .  ... 
doi:10.1142/9789812704016_0032 fatcat:dnawpqpxxrejjc62vgtu32fdvi

Page 1904 of Mathematical Reviews Vol. , Issue 2001C [page]

2001 Mathematical Reviews  
Liggett (1-UCLA; Los Angeles, CA) 2001¢:60160 60K35 60J10 Winkler, Peter |Winkler, Peter M.] (1-BELL; Murray Hill, NJ) Dependent percolation and colliding random walks.  ...  , but only when the corresponding interval is crossed, and only in a fashion which does not depend on the future of the walk.  ... 

Limiting distribution of last passage percolation models [article]

Jinho Baik
2003 arXiv   pre-print
We survey some results and applications of last percolation models of which the limiting distribution can be evaluated.  ...  Acknowledgments The author would like to thank Percy Deift and Michio Jimbo for kindly inviting him to the special session of integrable systems in the International Congress on Mathematical Physics.  ...  Random vicious walks The combinatorics of the longest increasing subsequence and the Plancherel measure have an interpretation as non-intersecting paths, which is sometimes called vicious walks [20] .  ... 
arXiv:math/0310347v2 fatcat:h5mkgisionbgznxleshn3lf2cm

Recurrent graphs where two independent random walks collide finitely often [article]

Manjunath Krishnapur, Yuval Peres
2004 arXiv   pre-print
We present a class of graphs where simple random walk is recurrent, yet two independent walkers meet only finitely many times almost surely.  ...  We also conjecture that the same property holds for some other graphs, including the incipient infinite cluster for critical percolation in Z^2.  ...  Acknowledgement: We thank Jeffrey Steif and Nina Gantert for encouragement.  ... 
arXiv:math/0406487v2 fatcat:bo2wbf4khnb7rha5bmwekt4oty

Recurrent Graphs where Two Independent Random Walks Collide Finitely Often

Manjunath Krishnapur, Yuval Peres
2004 Electronic Communications in Probability  
We present a class of graphs where simple random walk is recurrent, yet two independent walkers meet only finitely many times almost surely.  ...  We also conjecture that the same property holds for some other graphs, including the incipient infinite cluster for critical percolation in Z 2 .  ...  Acknowledgement: We thank Jeffrey Steif and Nina Gantert for encouragement.  ... 
doi:10.1214/ecp.v9-1111 fatcat:pzzbpqvuyfghzgmmicql25xabm

Self-organizing social hierarchy and villages in a challenging society

Masaru Tsujiguchi, Takashi Odagaki
2007 Physica A: Statistical Mechanics and its Applications  
in the self-organization of the hierarchy and villages.  ...  Our results indicate that among controlling processes of diffusion and fighting of individuals and relaxation of wealth, the trend of individuals challeninging to stronger neighbors plays the pivotal role  ...  The distance of one step of the random walk represents the mode of transportation.  ... 
doi:10.1016/j.physa.2006.08.026 fatcat:holvqzmpcvf2bfzoltw7jvchxe
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