Recurrence and windings of two revolving random walks

We study the winding behavior of random walks on two oriented square lattices. One common feature of these walks is that they are bound to revolve clockwise. We also obtain quantitative results of tran-sience/recurrence for each walk.

[1]  W. Werner,et al.  Stable windings , 2021 .

[2]  J. Br'emont,et al.  Planar random walk in a stratified quasi-periodic environment , 2020, 2007.01573.

[3]  Timothy Budd,et al.  Winding of simple walks on the square lattice , 2017, J. Comb. Theory, Ser. A.

[4]  F. Pène.  Random walks in random sceneries and related models , 2020 .

[5]  Random walk on the randomly-oriented Manhattan lattice , 2018, 1802.01558.

[6]  J. Br'emont.  Markov chains in a stratified environment , 2017 .

[7]  Serguei Popov,et al.  Non-homogeneous Random Walks: Lyapunov Function Methods for Near-Critical Stochastic Systems , 2016 .

[8]  Thomas S. Salisbury,et al.  Conditions for ballisticity and invariance principle for random walk in non-elliptic random environment , 2016, 1612.04761.

[9]  M. Menshikov,et al.  Heavy-Tailed Random Walks on Complexes of Half-Lines , 2016, 1610.00881.

[10]  J. L. Gall,et al.  Brownian Motion, Martingales, and Stochastic Calculus , 2016 .

[11]  Dimitri Petritis,et al.  Type Transition of Simple Random Walks on Randomly Directed Regular Lattices , 2012, Journal of Applied Probability.

[12]  F. Pène,et al.  Random walk in random environment in a two-dimensional stratified medium with orientations , 2011, 1110.4865.

[13]  Bruno Schapira,et al.  A local limit theorem for random walks in random scenery and on randomly oriented lattices , 2010, 1002.1878.

[14]  Gregory F. Lawler,et al.  Random Walk: A Modern Introduction , 2010 .

[15]  Transient random walk in with stationary orientations , 2009 .

[16]  Ira M. Gessel,et al.  Generalized Chung-Feller Theorems for Lattice Paths , 2009 .

[17]  Windings of planar random walks and averaged Dehn function , 2008, 0807.2192.

[18]  A functional limit theorem for a 2d-random walk with dependent marginals , 2007, 0705.3342.

[19]  N. Guillotin-Plantard,et al.  Transient Random Walks on 2D-Oriented Lattices@@@Transient Random Walks on 2D-Oriented Lattices , 2007 .

[20]  Transient Random Walks on 2D-Oriented Lattices , 2006, math/0601102.

[21]  M. Campanino,et al.  On the physical relevance of random walks: an example of random walks on a randomly oriented lattice , 2002, math/0201130.

[22]  M. Campanino,et al.  Random walks on randomly oriented lattices , 2001, math/0111305.

[23]  Zhan Shi.  Windings of Brownian motion and random walks in the plane , 1998 .

[24]  A. Shiryayev.  On Sums of Independent Random Variables , 1992 .

[25]  J. Faraway,et al.  Winding angle and maximum winding angle of the two-dimensional random walk , 1991, Journal of Applied Probability.

[26]  R. Durrett.  Probability: Theory and Examples , 1993 .

[27]  Pál Révész,et al.  Random walk in random and non-random environments , 1990 .

[28]  Claude J. P. Bélisle.  Windings of Random Walks , 1989 .

[29]  J. Pitman,et al.  Asymptotic Laws of Planar Brownian Motion , 1986 .

[30]  On D. Williams' “Pinching Method” and Some Applications , 1982 .

[31]  G. Matheron,et al.  Is transport in porous media always diffusive? A counterexample , 1980 .

[32]  J. Kemperman.  The oscillating random walk , 1974 .

[33]  David M. Miller,et al.  Handbook of Mathematical Functions With Formulas, Graphs and Mathematical Tables (National Bureau of Standards Applied Mathematics Series No. 55) , 1965 .

[34]  P. Erdos,et al.  Some problems concerning the structure of random walk paths , 1963 .

[35]  Frank Spitzer,et al.  Some theorems concerning 2-dimensional Brownian motion , 1958 .

[36]  Feller William,et al.  An Introduction To Probability Theory And Its Applications , 1950 .