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We consider the continuum version of the random field Ising model in onedimension: this model arises naturally as weak disorder scaling limit of theoriginal Ising model. Like for the Ising model, a spin configuration isconveniently described as a sequence of spin domains with alternating signs(domain-wall structure). We show that for fixed centered external field and asspin-spin couplings become large, the domain-wall structure scales to adisorder dependent limit that coincides with the infinite disorder fixed pointprocess introduced by D. S. Fisher in the context of zero temperature quantumIsing chains. In particular, our results establish a number of predictions thatone can find in [Fisher, Le Doussal and Monthus 2001]. The infinite disorderfixed point process for centered external field is equivalently described interms of the process of suitably selected extrema of a Brownian trajectoryintroduced and studied by J. Neveu and J. Pitman [Neveu and Pitman 1989]. Thischaracterization of the infinite disorder fixed point is one of the importantingredients of our analysis.

Infinite disorder renormalization fixed point for the continuum random field Ising chain