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We investigate the probabilities of large deviations for the position of the front in a stochastic model of the reaction $X+Y to 2X$ on the integer lattice in which $Y$ particles do not move while $X$ particles move as independent simple continuous time random walks of total jump rate $2$. For a wide class of initial conditions, we prove that a large deviations principle holds and we show that the zero set of the rate function is the interval $[0,v]$, where $v$ is the velocity of the front given by the law of large numbers. We also give more precise estimates for the rate of decay of the slowdown probabilities. Our results indicate a gapless property of the generator of the process as seen from the front, as it happens in the context of nonlinear diffusion equations describing the propagation of a pulled front into an unstable state.
Consider the symmetric exclusion process evolving on an interval and weakly interacting at the end-points with reservoirs. Denote by $I_{[0,T]} (cdot)$ its dynamical large deviations functional and by $V(cdot)$ the associated quasi-potential, defined
We consider a classical model related to an empirical distribution function $ F_n(t)=frac{1}{n}sum_{k=1}^nI_{{xi_kle t}}$ of $(xi_k)_{ige 1}$ -- i.i.d. sequence of random variables, supported on the interval $[0,1]$, with continuous distribution func
We give a quantitative analysis of clustering in a stochastic model of one-dimensional gas. At time zero, the gas consists of $n$ identical particles that are randomly distributed on the real line and have zero initial speeds. Particles begin to move
These notes survey the first and recent results on large deviations of Schramm-Loewner evolutions (SLE) with the emphasis on interrelations among rate functions and applications to complex analysis. More precisely, we describe the large deviations of
We derive the large deviation principle for radial Schramm-Loewner evolution ($operatorname{SLE}$) on the unit disk with parameter $kappa rightarrow infty$. Restricting to the time interval $[0,1]$, the good rate function is finite only on a certain