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pro vyhledávání: '"Carmona, Philippe"'
Autor:
Carmona, Philippe
The aim of this paper is to tackle part of the program set by Diekmann et al. in their seminal paper Diekmann et al. (2001). We quote "It remains to investigate whether, and in what sense, the nonlinear determin-istic model formulation is the limit o
Externí odkaz:
http://arxiv.org/abs/1804.04913
We review some recent results obtained in the framework of the 2-dimensional Interacting Self-Avoiding Walk (ISAW). After a brief presentation of the rigorous results that have been obtained so far for ISAW we focus on the Interacting Partially Direc
Externí odkaz:
http://arxiv.org/abs/1802.08745
Autor:
Carmona, Philippe, Pétrélis, Nicolas
We derive a functional central limit theorem for the excursion of a random walk conditioned on sweeping a prescribed geometric area. We assume that the increments of the random walk are integer-valued, centered, with a third moment equal to zero and
Externí odkaz:
http://arxiv.org/abs/1709.06448
Autor:
Carmona, Philippe, Pétrélis, Nicolas
In this paper we give a complete characterization of the scaling limit of the critical Interacting Partially Directed Self-Avoiding Walk (IPDSAW) introduced in Zwanzig and Lauritzen (1968). As the system size $L$ diverges, we prove that the set of oc
Externí odkaz:
http://arxiv.org/abs/1707.09628
Autor:
Carmona, Philippe
We give an exact expression for the partition function of a continuous time DPRE on a two points state space.
Externí odkaz:
http://arxiv.org/abs/1607.04443
Autor:
Carmona, Philippe, Pétrélis, Nicolas
This paper is dedicated to the investigation of a $1+1$ dimensional self-interacting and partially directed self-avoiding walk, usually referred to by the acronym IPDSAW and introduced in \cite{ZL68} by Zwanzig and Lauritzen to study the collapse tra
Externí odkaz:
http://arxiv.org/abs/1507.08332
Autor:
Carmona, Philippe, Pétrélis, Nicolas
Publikováno v:
The Annals of Applied Probability, 2019 Apr 01. 29(2), 875-930.
Externí odkaz:
https://www.jstor.org/stable/26581808
Autor:
Carmona, Philippe, Hu, Yueyun
We consider a random walk on $\Z$ that branches at the origin only. In the supercritical regime we establish a law of large number for the maximal position $M_n$. Then we determine all possible limiting law for the sequence $M_n -\alpha n$ where $\al
Externí odkaz:
http://arxiv.org/abs/1202.0637
We consider a discrete-time version of the parabolic Anderson model. This may be described as a model for a directed (1+d)-dimensional polymer interacting with a random potential, which is constant in the deterministic direction and i.i.d. in the d o
Externí odkaz:
http://arxiv.org/abs/1012.4653
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