In this paper we study the kinetics of diffusion-limited, pseudo-first-orderA + B -> B reactions in situations in which the particles' intrinsicreactivities vary randomly in time. That is, we suppose that the particles arebearing "gates" which interchange randomly and independently of each otherbetween two states - an active state, when the reaction may take place, and ablocked state, when the reaction is completly inhibited. We consider fourdifferent models, such that the A particle can be either mobile or immobile,gated or ungated, as well as ungated or gated B particles can be fixed atrandom positions or move randomly. All models are formulated on a$d$-dimensional regular lattice and we suppose that the mobile species performindependent, homogeneous, discrete-time lattice random walks. The modelinvolving a single, immobile, ungated target A and a concentration of mobile,gated B particles is solved exactly. For the remaining three models wedetermine exactly, in form of rigorous lower and upper bounds, the large-Nasymptotical behavior of the A particle survival probability. We also realizethat for all four models studied here such a probalibity can be interpreted asthe moment generating function of some functionals of random walk trajectories,such as, e.g., the number of self-intersections, the number of sites visitedexactly a given number of times, "residence time" on a random array of latticesites and etc. Our results thus apply to the asymptotical behavior of thecorresponding generating functions which has not been known as yet.
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