47 problems

Let $rho0: mathbb{R}rightarrow[0,1]$ be an initial density profile, and let ${nu^{epsilon}}{epsiloninmathbb{R}{0}}$ be probability measures on the configuration space…

Let $S_n$ be the symmetric group, and let $\psi_w$ denote the unnormalized steady state probability associated with a permutation $w\in S_n$ in the inhomogeneous TASEP. Assume that…

Let $rho ameq{}(0,1)$ be the stationary Bernoulli density, let $mathbb{P}rho$ be the corresponding TASEP path measure, and let $ht(j)$ be the height function. For $winmathbb{R}$, d…

Let $\rho_-$ and $\rho_+$ be the left and right Bernoulli densities for the TASEP, let $\bar h(y)$ be the hydrodynamic limiting height profile, and let $h_t(j)$ be the height at ti…

Consider a finite multi-floor TASEP with $c\ge 1$ floors and attempted particle arrival and departure rates $\alpha>0$ and $\beta>0$. Let … and let … Assume condition (a): $L^*$ co…

Let $L$ denote the system size and let $\mathcal{C}_{t}$ be the critical region at time $t$. In equilibrium, the pointer traverses the system and the critical region on the corresp…

Let an impurity in the totally asymmetric simple exclusion process have jumping rates $b1$ and $b2$, and initially be located at the interface of a $1$-$0$ profile. Assume that…

Let $n$ be a positive integer, let $\lambda=(\lambda_1\geq\cdots\geq\lambda_n\geq 0)$ be a partition, and consider the multispecies totally asymmetric simple exclusion process (TAS…

Let $K_1$ be the product of the first three matrices in the displayed factorization of the TASEP kernel, and let $K_2$ be the operator defined by … Here the operators act on the in…

Convergence conjecture. For $\alpha>\frac12$, the half-line open TASEP with step initial condition $\eta_t^{\mathrm{step}}$ converges to the probability measure…

In the setting of the section, consider right Bernoulli TASEP with sequential updates and an additional caterpillar of length $b\varepsilon^{-1/2}$ placed at distance…

Consider discrete-time right Bernoulli TASEP with sequential updates and an additional caterpillar of length $M=b\varepsilon^{-1/2}+c$ placed at distance $M'\geq M-1$ from the righ…

Let $w\in S_n$ be a state of the inhomogeneous TASEP, and let $\psi_w$ denote its renormalized steady state probability in the specialization $y_i=0$. Let the monomial factor be th…

Let $n$) be a positive integer and consider the inhomogeneous TASEP on a ring of size $n$, with state space $\operatorname{St}(n)$ identified with the symmetric group $S_n$. Let…

Consider TASEP with a reservoir of rate $\lambda=\rho q$ for some $\rho \in (0,\infty)$, and suppose that a flow rule holds for a flow of strength $q$. Let $\pi_{\lambda}$ be the e…

Consider the open totally asymmetric simple exclusion process (TASEP) on a chain of length $n$, with entry and exit rates $\beta$ and $\beta$? The maximal-current phase is the para…

Let $\rho$ be the particle density, let $h$ be the critical density, let $\phi(\rho;n)$ be the finite-$n$ typical flux, and let $\phi^*$ be the maximal-equilibrium-state flux. Let…

Let $n$ be a non-negative integer. For independent standard Brownian bridges $b_0,\ldots,b_{2n}$, define … Here $b$ is a standard Brownian bridge whose average is represented by…

Let $n$ be a non-negative integer. For independent standard Brownian bridges $b_0,\ldots,b_{2n}$, define … Here $\max$ denotes the maximum over the bridge parameter. Let…

Let $n$ be a non-negative integer and let $h_0$ be an arbitrary sufficiently regular continuous function satisfying … For independent standard Brownian bridges $b_1,\ldots,b_n$, de…

Let $h(x,t;h_0)$ and $\tilde{h}(x,t;\mathcal{H}_0)$ denote the height fluctuations with initial conditions $h_0$ and $\mathcal{H}_0$, respectively. For a function $\mathfrak{H}$ an…

Consider TASEP with a slow bond at the origin, and let the process start from the step initial condition. To the right of the origin, let the asymptotic particle density be denoted…

Consider TASEP on $\mathbb{Z}$ in which the bond jump rates are independent and identically distributed, with a fraction of bonds having rates distributed according to $Q$ supporte…

Let $\boldsymbol\tau$ and $\boldsymbol\nu$ be the model parameters, let $\psi_{\bf w}(\boldsymbol\tau,\boldsymbol\nu)$ denote the component associated with a particle configuration…

Let $\boldsymbol\tau=\{\tau_\alpha\}$ be the collection of model parameters, and consider the stationary probabilities of particle configurations, normalized by a partition functio…