Maximal Displacement for Bridges of Random Walks in a Random Environment (2009)
Gantert, Nina, Peterson, Jonathon
It is well known that the distribution of simple random walks on $\bf{Z}$ conditioned on returning to the origin after $2n$ steps does not depend on $p= P(S_1 = 1)$, the probability of moving to the...
Survival and Growth of a Branching Random Walk in Random Environment (2009)
Bartsch, Christian, Gantert, Nina, Kochler, Michael
We consider a particular Branching Random Walk in Random Environment (BRWRE) on $N_0$ started with one particle at the origin. Particles reproduce according to an offspring distribution (which...
Survival time of random walk in random environment among soft obstacles (2009)
Gantert, Nina; University Of Munster; Gantert@math.uni-muenster.de, Popov, Serguei; Universidade De São Paulo; Popov@ime.usp.br, Vachkovskaia, Marina; Universidade De Campinas; Marinav@ime.unicamp.br
We consider a Random Walk in Random Environment (RWRE) moving in an i.i.d. random field of obstacles. When the particle hits an obstacle, it disappears with a positive probability. We obtain quenched...
Survival of branching random walks in random environment (2008)
Gantert, Nina, Müller, Sebastian, Popov, Serguei, Vachkovskaia, Marina
We study survival of nearest-neighbour branching random walks in random environment (BRWRE) on $\mathbb{Z}$. A priori there are three different regimes of survival: global survival, local survival,...
Asymptotics for the survival probability in a killed branching random walk (2008)
Gantert, Nina, Hu, Yueyun, Shi, Zhan
Consider a discrete-time one-dimensional supercritical branching random walk. We study the probability that there exists an infinite ray in the branching random walk that always lies above the line...
Survival time of random walk in random environment among soft obstacles (2008)
Gantert, Nina, Popov, Serguei, Vachkovskaia, Marina
We consider a Random Walk in Random Environment (RWRE) moving in an i.i.d.\ random field of obstacles. When the particle hits an obstacle, it disappears with a positive probability. We obtain...
On slowdown and speedup of transient random walks in random environment (2008)
Fribergh, Alexander, Gantert, Nina, Popov, Serguei
We consider one-dimensional random walks in random environment which are transient to the right. Our main interest is in the study of the sub-ballistic regime, where at time $n$ the particle is...
Valleys and the maximum local time for random walk in random environment (2008)
Amir Dembo, Nina Gantert, Zhan Shi
Abstract Let,(n; x) be the local time at x for a recurrent one-dimensional random walk in random environment after n steps, and consider the maximum, \Lambda (n) = maxx,(n; x). It is known that lim...
Limit laws for biased random walks on a Galton-Watson tree with leaves (2007)
Fribergh, Alexander, Gantert, Nina
A mistake has been pointed out to us. The announced result does not hold. We withdraw for the moment and apologize.
Limit laws for biased random walks on a Galton-Watson tree with leaves (2007)
Fribergh, Alexander, Gantert, Nina
A mistake has been pointed out to us. The announced result does not hold. We withdraw for the moment and apologize.
Limit laws for biased random walks on a Galton-Watson tree with leaves (2007)
Fribergh, Alexander, Gantert, Nina
We consider an outwardly $\beta$-biased random walk $X_n$ on a Galton-Watson tree with leaves in the sub-ballistic regime. We prove that $X_n/n^{\gamma}$ convergences in law and we characterize the...
Biased random walks on a Galton-Watson tree with leaves (2007)
Arous, Gérard Ben, Fribergh, Alexander, Gantert, Nina, Hammond, Alan
We consider a biased random walk $X_n$ on a Galton-Watson tree with leaves in the sub-ballistic regime. We prove that there exists an explicit constant $\gamma= \gamma(\beta) \in (0,1)$, depending on...
Ofer Zeitouni December, Nina Gantert, Ofer Zeitouni
Suppose that the integers are assigned i.i.d. random variables f! x g (taking values in the unit interval), which serve as an environment. This environment defines a random walk fX n g (called a...
A Note on Logarithmic Tail Asymptotics and Mixing (2007)
Let Y 1 ; Y 2 ; : : : be a stationary, ergodic sequence of non-negative random variables with heavy tails. Under mixing conditions, we derive logarithmic tail asymptotics for the distributions of the...
The infinite valley for a recurrent random walk in random environment (2007)
Gantert, Nina, Peres, Yuval, Shi, Zhan
We consider a one-dimensional recurrent random walk in random environment (RWRE). We show that the - suitably centered - empirical distributions of the RWRE converge weakly to a certain limit law...
Biased random walks on a Galton-Watson tree with leaves (2007)
Ben Arous, Gérard, Fribergh, Alexander, Gantert, Nina, Hammond, Alan
We consider a biased random walk $X_n$ on a Galton-Watson tree with leaves in the sub-ballistic regime. We prove that there exists an explicit constant $\gamma= \gamma(\beta) \in (0,1)$, depending on...
Biased random walks on a Galton-Watson tree with leaves (2007)
Ben Arous, Gérard, Fribergh, Alexander, Gantert, Nina, Hammond, Alan
We consider a biased random walk $X_n$ on a Galton-Watson tree with leaves in the sub-ballistic regime. We prove that there exists an explicit constant $\gamma= \gamma(\beta) \in (0,1)$, depending on...
Annealed deviations of random walk in random scenery (2007)
Nina Gantert, Wolfgang König, Zhan Shi
Abstract: Let (Zn)n∈N be a d-dimensional random walk in random scenery, i.e., Zn = � n−1 k=0 Y (Sk) with (Sk)k∈N0 a random walk in Zd and (Y (z)) z∈Z d an i.i.d. scenery, independent of the...
Deviations of a random walk in a random scenery with stretched exponential tails (2006)
be a d-dimensional random walk in random scenery, i.e., Zn = � n−1 k=0 YSk with (Sk)k∈N0 a random walk in Zd and (Yz) z∈Z d an i.i.d. scenery, independent of the walk. We assume that the...
The critical Branching Markov Chain is transient (2005)
Gantert, Nina, Mueller, Sebastian
We investigate recurrence and transience of Branching Markov Chains (BMC) in discrete time. Branching Markov Chains are clouds of particles which move (according to an irreducible underlying Markov...
Valleys and the maximum local time for random walk in random environment (2005)
Dembo, Amir, Gantert, Nina, Peres, Yuval, Shi, Zhan
Let $\xi(n, x)$ be the local time at $x$ for a recurrent one-dimensional random walk in random environment after $n$ steps, and consider the maximum $\xi^*(n) = \max_x \xi(n,x)$. It is known that...
Deviations of a random walk in a random scenery with stretched exponential tails (2004)
Van Der Hofstad, Remco, Gantert, Nina, K{ö}nig, Wolfgang
Let (Z_n)_{n\in\N_0} be a d-dimensional random walk in random scenery, i.e., Z_n=\sum_{k=0}^{n-1}Y_{S_k} with (S_k)_{k\in\N_0} a random walk in Z^d and (Y_z)_{z\in Z^d} an i.i.d. scenery, independent...
Annealed deviations of random walk in random scenery (2004)
Gantert, Nina, König, Wolfgang, Shi, Zhan
Let $(Z_n)_{n\in\N}$ be a $d$-dimensional {\it random walk in random scenery}, i.e., $Z_n=\sum_{k=0}^{n-1}Y(S_k)$ with $(S_k)_{k\in\N_0}$ a random walk in $\Z^d$ and $(Y(z))_{z\in\Z^d}$ an i.i.d....
Large deviations for random walk in random environment with holding times (2004)
Dembo, Amir, Gantert, Nina, Zeitouni, Ofer
Suppose that the integers are assigned the random variables $\{\omega_x,\mu_x\}$ (taking values in the unit interval times the space of probability measures on $\reals_+$), which serve as an...
The speed of biased random walk on percolation clusters (2002)
Berger, Noam, Gantert, Nina, Peres, Yuval
We consider biased random walk on supercritical percolation clusters in $\Z^2$. We show that the random walk is transient and that there are two speed regimes: If the bias is large enough, the random...
Large deviations for random walk in random environment with holding times, preprint (2002)
Amir Dembo, Nina Gantert, Ofer Zeitouni
Suppose that the integers are assigned the random variables {ωx,µx} (taking values in the unit interval times the space of probability measures on R+), which serve as an environment. This...
Large Deviations for Random Walk in Random Environment with Holding Times (2002)
Amir Dembo, Nina Gantert, Ofer Zeitouni
Suppose that the integers are assigned the random variables f! x ; x g (taking values in the unit interval times the space of probability measures on R+ ), which serve as an environment. This...
Large Deviations for Random Walk in Random Environment with Holding Times (2002)
Amir Dembo, Nina Gantert, Ofer Zeitouni
Suppose that the integers are assigned random variables f! x ; x g (taking values in the unit interval times probability measures on R+ ), which serve as an environment. This environment de nes a...
The maximum of a branching random walk with semiexponential increments (2000)
We consider an in .nite Galton–Watson tree $\Gamma$ and label the vertices $v$ with a collection of i.i.d.random variables $(Y_v)_{v \in \Gamma}$. In the case where the upper tail of the...
The Maximum of a Branching Random Walk With Semiexponential Increments (1999)
: We consider an innite Galton-Watson tree and label the vertices v with a collection of i.i.d. random variables (Y v ) v2 . In the case where the upper tail of the distribution of Y v is...
Subexponential Tail Asymptotics for a Random Walk With Randomly Placed One-Way Nodes (1999)
: Let p 2]0; 1=2] and assign to the integers random variables f! x g, taking only the two values 1 and p, which serve as an environment. This environment denes a random walk fX n g which, when at x,...
Francis Comets, Nina Gantert, Ofer Zeitouni
: Suppose that the integers are assigned random variables f! i g (taking values in the unit interval), which serve as an environment. This environment denes a random walk fXng (called a RWRE) which,...
Functional Erdős-Renyi laws for semiexponential random variables (1998)
For an i.i.d. sequence of random variables with a semiexponential distribution, we give a functional form of the Erdös–Renyi law for partial sums. In contrast to the classical case, that is, the...
Quenched Sub-Exponential Tail Estimates for One-Dimensional Random Walk in Random Environment (1998)
Suppose that the integers are assigned i.i.d. random variables f! x g (taking values in the unit interval), which serve as an environment. This environment defines a random walk fX n g (called a...
Francis Comets, Nina Gantert, Ofer Zeitouni
: Suppose that the integers are assigned random variables f! i g (taking values in the unit interval), which serve as an environment. This environment defines a random walk fXng (called a RWRE)...
Large Deviations for One-Dimensional Random Walk in a Random Environment - a Survey (1998)
Suppose that the integers are assigned i.i.d. random variables f! x g (taking values in the unit interval), which serve as an environment. This environment defines a random walk fX n g (called a...
Functional Erdös-Renyi laws for semiexponential random variables (1998)
For an i.i.d. sequence of random variables with a semiexponential distribution, we give a functional form of the Erdos-Renyi law for partial sums. In contrast to the classical case, i.e. the case...
Francis Comets, Nina Gantert, Ofer Zeitouni
: Suppose that the integers are assigned random variables f! i g (taking values in the unit interval), which serve as an environment. This environment defines a random walk fXng (called a RWRE)...
Francis Comets Nina, Nina Gantert, Ofer Zeitouni
Suppose that the integers are assigned random variables f! i g (taking values in the unit interval), which serve as an environment. This environment de nes a random walk fXng (called a RWRE) which,...
Entropy minimization and Schrödinger processes in infinite dimensions (1997)
Schrödinger processes are defined as mixtures of Brownian bridges which preserve the Markov property. In finite dimensions, they can be characterized as $h$-transforms in the sense of Doob for some...
Abstract. Schrodinger processes are defined as mixtures of Brownian bridges which preserve the Markov property. In finite dimensions, they can be characterized as h-transforms in the sense of Doob...
Einige grobe Abweichungen der Brownschen Bewegung / (1991)
Thesis (Doctoral)--Universität Bonn, 1991.
Einige grosse Abweichungen der Brownschen Bewegung /--vorgelegt von Nina Gantert. (1991)
Thesis (Doctoral)--Rheinische Friedrich-Wilhelms-Universität Bonn, 1991.
A note on logarithmic tail asymptotics and mixing
Let Y1,Y2,... be a stationary, ergodic sequence of non-negative random variables with heavy tails. Under mixing conditions, we derive logarithmic tail asymptotics for the distributions of the...