Topology of the Support of the Two-Dimensional Lattice Random Walk

1996 ◽  
Vol 77 (6) ◽  
pp. 992-995 ◽  
Author(s):  
S. Caser ◽  
H. J. Hilhorst
Keyword(s):  
Random Walk ◽  
Two Dimensional ◽  
Dimensional Lattice ◽  
Lattice Random Walk

Random walk and SU(2) Clebsch–Gordon coefficients

1979 ◽  
Vol 57 (11) ◽  
pp. 2050-2051
Author(s):  
F. Lemire ◽  
J. Patera
Keyword(s):  
Random Walk ◽  
Generating Function ◽  
Transition Function ◽  
Two Dimensional ◽  
Dimensional Lattice ◽  
New Interpretation ◽  
Source Of Information

This article contains a new interpretation of the values of the SU(2) Clebsch–Gordon coefficients (CGC). It is shown that a given CGC C(l1,l2,l;m1,m2,m) can be understood as a transition function for a random walk on a two dimensional lattice between the origin and the point (m1,m2) in l1 + l2 + l steps. This interpretation is based on the generating function for the CGC which has previously been shown to be a rich and concise source of information on the CGC.

A correlated random walk model for two-dimensional diffusion

1984 ◽  
Vol 21 (2) ◽  
pp. 233-246 ◽  
Author(s):  
Robin Henderson ◽  
Eric Renshaw ◽  
David Ford
Keyword(s):  
Random Walk ◽  
Transition Probabilities ◽  
Exact Expression ◽  
Dispersion Matrix ◽  
Two Dimensional ◽  
Correlated Random Walk ◽  
Dimensional Diffusion ◽  
Step Transition ◽  
Lattice Random Walk ◽  
Previous Step

A two-dimensional lattice random walk is studied in which, at each stage, the direction of the next step is correlated to that of the previous step. An exact expression is obtained from the characteristic function for the dispersion matrix of the n-step transition probabilities, and the limiting diffusion equation is derived.

A correlated random walk model for two-dimensional diffusion

1984 ◽  
Vol 21 (02) ◽  
pp. 233-246 ◽  
Author(s):  
Robin Henderson ◽  
Eric Renshaw ◽  
David Ford
Keyword(s):  
Random Walk ◽  
Transition Probabilities ◽  
Exact Expression ◽  
Dispersion Matrix ◽  
Two Dimensional ◽  
Correlated Random Walk ◽  
Dimensional Diffusion ◽  
Step Transition ◽  
Lattice Random Walk ◽  
Previous Step

A two-dimensional lattice random walk is studied in which, at each stage, the direction of the next step is correlated to that of the previous step. An exact expression is obtained from the characteristic function for the dispersion matrix of the n-step transition probabilities, and the limiting diffusion equation is derived.

A note on the recurrence of a correlated random walk

1983 ◽  
Vol 20 (03) ◽  
pp. 696-699 ◽  
Author(s):  
Robin Henderson ◽  
Eric Renshaw ◽  
David Ford
Keyword(s):  
Random Walk ◽  
Two Dimensional ◽  
Correlated Random Walk ◽  
Analytical Proof ◽  
Lattice Random Walk

A non-analytical proof of recurrence is obtained via an embedding procedure for a two-dimensional correlated lattice random walk.

A note on the recurrence of a correlated random walk

1983 ◽  
Vol 20 (3) ◽  
pp. 696-699 ◽  
Author(s):  
Robin Henderson ◽  
Eric Renshaw ◽  
David Ford
Keyword(s):  
Random Walk ◽  
Two Dimensional ◽  
Correlated Random Walk ◽  
Analytical Proof ◽  
Lattice Random Walk

A non-analytical proof of recurrence is obtained via an embedding procedure for a two-dimensional correlated lattice random walk.

scholarly journals DISCRETE AND CONTINUUM APPROACHES TO THREE-DIMENSIONAL QUANTUM GRAVITY

1991 ◽  
Vol 06 (39) ◽  
pp. 3591-3600 ◽  
Author(s):  
HIROSI OOGURI ◽  
NAOKI SASAKURA
Keyword(s):  
Gauge Theory ◽  
Moduli Space ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Analogue Model ◽  
Gauge Invariant ◽  
Invariant Functions ◽  
Dimensional Lattice ◽  
Chern Simons ◽  
Dimensional Surface

It is shown that, in the three-dimensional lattice gravity defined by Ponzano and Regge, the space of physical states is isomorphic to the space of gauge-invariant functions on the moduli space of flat SU(2) connections over a two-dimensional surface, which gives physical states in the ISO(3) Chern–Simons gauge theory. To prove this, we employ the q-analogue of this model defined by Turaev and Viro as a regularization to sum over states. A recent work by Turaev suggests that the q-analogue model itself may be related to an Euclidean gravity with a cosmological constant proportional to 1/k2, where q=e2πi/(k+2).

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