Résumé /Abstract:
Since its introduction by FRANK SPITZER nearly forty years ago, the asymmetric simple exclusion process (ASEP) has become the "default stochastic model for transport phenomena." Some have called the ASEP the "Ising model for nonequilibrium physics." In ASEP on the integer lattice $\bZ$ particles move according to two rules: (1) A particle at $x$ waits an exponential time with parameter one (independently of all the other particles), and then it chooses $y$ with probability $p(x,y)$; (2) If $y$ is vacant at that time it moves to $y$, while if $y$ is occupied it remains at $x$ and restarts the clock. †The adjective "simple" refers to the fact that allowed jumps are one step to the right, $p(x,x+1)=p$, or one step to the left, $p(x,x-1)=1-p=q$. The asymmetric condition means $p\neq q$ so that there is a net drift to either the right or the left. The first lecture will discuss the integrable structure of ASEP on $\bZ$. †We show how ideas from Bethe Ansatz can be applied in a novel way to ASEP. The second lecture continues with a discussion of some basic limit theorems which prove KPZ Universality for ASEP. Le café sera servi à 15h30 au Salon Maurice-L'Abbé - salle 6245 Coffee will be served at 3:30 pm in Salon Maurice-L'Abbé - Room 6245
Résumé /Abstract: Since its introduction by FRANK SPITZER nearly forty years ago, the asymmetric simple exclusion process (ASEP) has become the "default stochastic model for transport phenomena." Some have called the ASEP the "Ising model for nonequilibrium physics." In ASEP on the integer lattice $\bZ$ particles move according to two rules: (1) A particle at $x$ waits an exponential time with parameter one (independently of all the other particles), and then it chooses $y$ with probability $p(x,y)$; (2) If $y$ is vacant at that time it moves to $y$, while if $y$ is occupied it remains at $x$ and restarts the clock. †The adjective "simple" refers to the fact that allowed jumps are one step to the right, $p(x,x+1)=p$, or one step to the left, $p(x,x-1)=1-p=q$. The asymmetric condition means $p\neq q$ so that there is a net drift to either the right or the left. The first lecture will discuss the integrable structure of ASEP on $\bZ$. †We show how ideas from Bethe Ansatz can be applied in a novel way to ASEP. The second lecture continues with a discussion of some basic limit theorems which prove KPZ Universality for ASEP.
Coffee will be served at 3:30 pm in Salon Maurice-L'Abbé - Room 6245
Résumé / Abstract: This lecture, designed for a general audience, will survey "exactly solvable" models in statistical physics. The three main examples will be the 2D Ising model, Random Matrix Models, and the Asymmetric Simple Exclusion Process. The underlying theme is the connection with integrable differential equations of Painlevé type. Le café sera servi à 15h30 et une réception suivra la conférence au Salon Maurice-L'Abbé - salle 6245 |