10 papers · 1 filter
Scaling Limit of Sub-ballistic 1D Random Walk among Biased Conductances: a Story of Wells and Walls
Quentin Berger, Michele Salvi
We consider a one-dimensional random walk among biased i.i.d. conductances, in the case where the random walk is transient but sub-ballistic: this occurs when the conductances have…
Disorder and denaturation transition in the generalized Poland-Scheraga model
Quentin Berger, Giambattista Giacomin, Maha Khatib
We investigate the generalized Poland-Scheraga model, which is used in the bio-physical literature to model the DNA denaturation transition, in the case where the two strands are a…
Strong renewal theorems and local large deviations for multivariate random walks and renewals
Quentin Berger
We study a random walk on (), in the domain of attraction of an operator-stable distribution with index $\boldsymbolα=(α_1,\ldots,α_d) \in (0…
Entropy-controlled Last-Passage Percolation
Quentin Berger, Niccolo Torri
In the present article we consider a natural generalization of Hammersley's Last Passage Percolation (LPP) called Entropy-controlled Last Passage Percolation (E-LPP), where points…
Beyond Hammersley's Last-Passage Percolation: a discussion on possible local and global constraints
Quentin Berger, Niccolo Torri
Hammersley's Last-Passage Percolation (LPP), also known as Ulam's problem, is a well-studied model that can be described as follows: consider points chosen uniformly and indepe…
Directed polymers in heavy-tail random environment
Quentin Berger, Niccolo Torri
We study the directed polymer model in dimension when the environment is heavy-tailed, with a decay exponent . We give all possible scaling limits of the model i…