Several recent works have shown that the onedimensional fully asymmetric exclusion model, which describes a ystem of panicles hopping in a preferred direction with hard core interactions, can be solved exactb in the case of open boundaries. Here we present a new approach based on representing the weights of each mnfiguration in the steady state as a product of noncommuting matrices. Wth this approach the whole solution of the problem is reduced to finding two matrices and two vectors which satisQ ve'y simple algebraic NI= We obtain several explicit toms for these noncommuting matrices which are, in the general case. infinite-dimensional. Our approach allows exam expresions to be derived for the current and density profiles. Finally we discuss h'efly two possible generalizations of our results: the pmblem of panially asymmetric exclusion and the case of a mixture of two kinds of panicles.

We study simple diffusion where a particle stochastically resets to its initial position at a constant rate r. A finite resetting rate leads to a nonequilibrium stationary state with non-Gaussian fluctuations for the particle position. We also show that the mean time to find a stationary target by a diffusive searcher is finite and has a minimum value at an optimal resetting rate r * . Resetting also alters fundamentally the late time decay of the survival probability of a stationary target when there are multiple searchers: while the typical survival probability decays exponentially with time, the average decays as a power law with an exponent depending continuously on the density of searchers.PACS numbers: 87.23.Ge 'Stochastic resetting' is a rather common process in everyday life. Consider searching for some target such as, for example, a face in a crowd or one's misplaced keys at home. A natural tendency is, on having searched unsuccessfully for a while, to return to the starting point and recommence the search. In this Letter we explore the consequences of such resetting on perhaps the most simple and common process in nature, namely, the diffusion of a single or a multiparticle system. We show that a nonzero rate of resetting has a rather rich and dramatic effect on the diffusion process.The first major effect of resetting shows up in the position distribution of the diffusing particle. In the absence of resetting, it has the usual Gaussian distribution whose width grows diffusively ∼ √ t with time. Upon switching on a nonzero resetting rate r to its initial position, this time-dependent Gaussian distribution gives way to a globally current-carrying nonequilibrium stationary state (NESS) with non-Gaussian fluctuations, given in Eq. (2). The process of resetting manifestly violates detailed balance and thus provides an appealingly simple example of a NESS.Resetting also has a profound consequence on the firstpassage properties of a diffusing particle. The study of first-passage problems and survival probabilities of diffusing particles arises in diverse subjects such as in reactiondiffusion kinetics, predator-prey dynamics [1], as well as in persistence in nonequilibrium systems [2]. Such problems are fundamental to nonequilibrium statistical mechanics as they involve irreversible processes not obeying detailed balance. Related models are also relevant to the study of search strategies in ecology or sampling techniques for the characterisation of complex networks. For example, intermittent searches involve diffusive motion combined with long range movements of the searcher and mimic the scan and relocation phases of foraging animals [3][4][5][6][7][8]. A well-studied problem is the mean time for a stationary target at the origin to be absorbed by a single diffusing particle (trap) or a team of diffusing traps distributed with uniform density. Many significant results, such as the fact that the mean time to find the target by a single diffusing particle diverges and that the survival probabilty of the ta...