Dependent Double Branching Annihilating Random Walk

586 Pages·2015·1.8 MB·English

by  Márton Balázs

Models Scaled Meanfield Positiverecurrence Proof
Dependent Double Branching Annihilating
Random Walk
Jointwith
AttilaLa´szlo´ Nagy
Ma´rton Bala´zs
UniversityofBristol
New Perspectives in Analysis and Probability
University of Sussex
6th March, 2015.
Models Scaled Meanfield Positiverecurrence Proof
Attractive and non-attractive models
Totally asymmetric simple exclusion process
A ⊕ ⊖ 0 model
Totally asymmetric zero range process
On large scales
Shocks
Rarefaction waves
A mean field version
Positive recurrence
Two words on the proof
Models Scaled Meanfield Positiverecurrence Proof TASEP ⊕⊖0 TAZRP
The totally asymmetric simple exclusion process
◦ ◦ ◦ ◦• ◦• ◦ ◦• ◦
-3 -2 -1 0 1 2 3 4 i
ω(0) ∼ Bernoulli(̺) product distribution.
i
Models Scaled Meanfield Positiverecurrence Proof TASEP ⊕⊖0 TAZRP
The totally asymmetric simple exclusion process
◦ ◦ ◦ ◦• ◦• ◦ ◦• ◦
-3 -2 -1 0 1 2 3 4 i
ω(0) ∼ Bernoulli(̺) product distribution.
i
Particles step to the right with rate 1,
unless the destination site is occupied.
Models Scaled Meanfield Positiverecurrence Proof TASEP ⊕⊖0 TAZRP
The totally asymmetric simple exclusion process
◦ ◦ ◦ ◦• ◦• ◦ •◦ ◦
-3 -2 -1 0 1 2 3 4 i
ω(0) ∼ Bernoulli(̺) product distribution.
i
Particles step to the right with rate 1,
unless the destination site is occupied.
Models Scaled Meanfield Positiverecurrence Proof TASEP ⊕⊖0 TAZRP
The totally asymmetric simple exclusion process
◦ ◦ ◦ ◦• ◦• ◦ •◦ ◦
-3 -2 -1 0 1 2 3 4 i
ω(0) ∼ Bernoulli(̺) product distribution.
i
Particles step to the right with rate 1,
unless the destination site is occupied.
Models Scaled Meanfield Positiverecurrence Proof TASEP ⊕⊖0 TAZRP
The totally asymmetric simple exclusion process
◦ ◦ ◦ ◦• ◦• ◦ ◦• ◦
-3 -2 -1 0 1 2 3 4 i
ω(0) ∼ Bernoulli(̺) product distribution.
i
Particles step to the right with rate 1,
unless the destination site is occupied.
Models Scaled Meanfield Positiverecurrence Proof TASEP ⊕⊖0 TAZRP
The totally asymmetric simple exclusion process
◦ ◦ ◦ ◦• ◦• ◦ ◦• ◦
-3 -2 -1 0 1 2 3 4 i
ω(0) ∼ Bernoulli(̺) product distribution.
i
Particles step to the right with rate 1,
unless the destination site is occupied.
Models Scaled Meanfield Positiverecurrence Proof TASEP ⊕⊖0 TAZRP
The totally asymmetric simple exclusion process
◦ ◦ ◦ ◦• ◦ • ◦ ◦• ◦
-3 -2 -1 0 1 2 3 4 i
ω(0) ∼ Bernoulli(̺) product distribution.
i
Particles step to the right with rate 1,
unless the destination site is occupied.
Models Scaled Meanfield Positiverecurrence Proof TASEP ⊕⊖0 TAZRP
The totally asymmetric simple exclusion process
◦ ◦ ◦ ◦• ◦ •◦ ◦• ◦
-3 -2 -1 0 1 2 3 4 i
ω(0) ∼ Bernoulli(̺) product distribution.
i
Particles step to the right with rate 1,
unless the destination site is occupied.