Related papers: Delocalization of Polymers in Lower Tail Large Dev…
A well-known question in planar first-passage percolation concerns the convergence of the empirical distribution of weights as seen along geodesics. We demonstrate this convergence for an explicit model, directed last-passage percolation on…
We establish sharp large deviation principles for cumulative rewards associated with a discrete-time renewal model, supposing that each renewal involves a broad-sense reward taking values in a real separable Banach space. The framework we…
We analyze the geometrical structure of the passage times in the last passage percolation model. Viewing the passage time as a piecewise linear function of the weights we determine the domains of the various pieces, which are the subsets of…
In classical percolation theory, the van den Berg-Kesten (BK) inequality is a fundamental tool that shows that disjoint events induce negative conditionings on each other. The inequality also holds in the context of last passage percolation…
We study the critical behavior of the component sizes for the configuration model when the tail of the degree distribution of a randomly chosen vertex is a regularly-varying function with exponent $\tau-1$, where $\tau\in (3,4)$. The…
The well-known "Janson's inequality" gives Poisson-like upper bounds for the lower tail probability \Pr(X \le (1-\eps)\E X) when X is the sum of dependent indicator random variables of a special form. We show that, for large deviations,…
We study the random geometry of first passage percolation on the complete graph equipped with independent and identically distributed edge weights, continuing the program initiated by Bhamidi and van der Hofstad [6]. We describe our results…
Because of a close blood relationship between directed percolation & directed polymers in random media, the latter's journey to asymptotic scaling can be greatly retarded by an uninformed choice of departure point; i.e., the bare-bond PDF…
We study a (1+1)-dimensional directed polymer in a random environment on the integer lattice with log-gamma distributed weights. Among directed polymers, this model is special in the same way as the last-passage percolation model with…
Noise-induced transitions between multistable states happen in a multitude of systems, such as species extinction in biology, protein folding, or tipping points in climate science. Large deviation theory is the rigorous language to describe…
We study the lower tail large deviation problem for subgraph counts in a random graph. Let $X_H$ denote the number of copies of $H$ in an Erd\H{o}s-R\'enyi random graph $\mathcal{G}(n,p)$. We are interested in estimating the lower tail…
We study the dynamics of a polymer or a D-dimensional elastic manifold diffusing and convected in a non-potential static random flow (the ``randomly driven polymer model''). We find that short-range (SR) disorder is relevant for d < 4 for…
We study moderate deviations in the exponential corner growth model, both in the bulk setting and the increment-stationary setting. The main results are sharp right-tail bounds on the last-passage time and the exit point of the…
In the real world, long-tailed data distributions are prevalent, making it challenging for models to effectively learn and classify tail classes. However, we discover that in the field of drug chemistry, certain tail classes exhibit higher…
In this paper, we study large time large deviations for the height function $\mathfrak{h}(x,t)$ of the $q$-deformed polynuclear growth introduced in ABW22 [arXiv:2108.06018]. We show that the upper-tail deviations have speed $t$ and derive…
We consider inhomogeneous spatial random graphs on the real line. Each vertex carries an i.i.d. weight and edges are drawn such that short edges and edges to vertices with large weights occur with higher probability. This allows the study…
In this paper we propagate a large deviations approach for proving limit theory for (generally) multivariate time series with heavy tails. We make this notion precise by introducing regularly varying time series. We provide general large…
We consider a one-dimensional directed polymer in a random potential which is characterized by the Gaussian statistics with the finite size local correlations. It is shown that the well-known Kardar's solution obtained originally for a…
We study discrete statistical mechanics systems perturbed by a random environment without a finite second moment. Specifically, we consider a random environment whose tail distribution satisfies $P[\omega > x] \sim x^{-\gamma}$ as $x \to…
We consider analytically as well as numerically the finite-size scaling behavior in the stationary state near the non-equilibrium phase transition of directed percolation within the mean field regime, i.e., above the upper critical…