What is Transient impact model?

A transient impact model prices an execution as the continuous-time propagator: trading at rate $v(s)$ moves the price at time $t$ by $\int_{s<t}G(t-s)\,v(s)\,ds$, so an execution $x_1,\dots,x_n$ at times $t_1,\dots,t_n$ costs $\tfrac12x^\top\Gamma x$ with $\Gamma_{ij}=G(|t_i-t_j|)$.