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VII: 24, 248-272, LNM 321 (1973)

**MÜRMANN, Michael G.**

A semi-Markovian model for the Brownian motion (Statistical mechanics)

A model for physical Brownian motion (the effect on a heavy particle of many interactions with light particles), originally proposed by Spitzer and Holley, in dimension 1, is studied in detail. The resulting process, whose construction is delicate, is non-Markovian

Comment: The last two pages of the manuscript (proof of Proposition 5 and References) were omitted at the production stage, and added as a loose sheet to vol. VIII, while another loose sheet contains an example. These sheets are not mentioned in the table of contents of vol. VIII

Keywords: Infinite particle systems

Nature: Original

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VII: 26, 284-290, LNM 321 (1973)

**ROST, Hermann**

Relaxation in infinite spin systems (Statistical mechanics)

The existence of a stochastic process describing an infinitely many interacting particle system is proved

Comment: This is related to Sullivan,*Zeit. für W-theorie,* **31**, 1974

Keywords: Interacting particle systems

Nature: Original

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IX: 26, 471-485, LNM 465 (1975)

**NAGASAWA, Masao**

Multiplicative excessive measures and duality between equations of Boltzmann and of branching processes (Markov processes, Statistical mechanics)

The author investigates the connection between the branching Markov processes constructed over some given Markov processes and a non-linear equation close to Boltzmann's equation. A special class of excessive measures for the branching Markov process is described and studied, as well as the corresponding dual processes

Comment: For other contributions by the same author devoted to the relation between branching process and non-linear equations, see 618, 1011

Keywords: Boltzmann equation, Branching processes

Nature: Original

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XXIX: 18, 194-201, LNM 1613 (1995)

**FRANCHI, Jacques**

Chaos multiplicatif : un traitement simple et complet de la fonction de partition (Statistical mechanics)

Introduced by Mandelbrot (*Comptes Rendus Acad. Sci. * **278**, 289--292, 1974), the model of multiplicative chaos has since been studied by several mathematicians and physicists. Using a trick of Kahane, this article presents a complete and elementary calculation of the pressure, thereby completing and simplifying previous work by Collet and Koukiou. Moreover it connects the critical temperature to the entropy, and gives a necessary and sufficient condition for finiteness of the critical temperature

Keywords: Multiplicative chaos, Partition function, Pressure, Critical temperature

Nature: Original

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XLIV: 18, 401-407, LNM 2046 (2012)

**MOURRAT, Jean-Christophe**

On the delocalized phase of the random pinning model (Statistical mechanics)

Keywords: Directed Polymer models, Partition function

Nature: Original

A semi-Markovian model for the Brownian motion (Statistical mechanics)

A model for physical Brownian motion (the effect on a heavy particle of many interactions with light particles), originally proposed by Spitzer and Holley, in dimension 1, is studied in detail. The resulting process, whose construction is delicate, is non-Markovian

Comment: The last two pages of the manuscript (proof of Proposition 5 and References) were omitted at the production stage, and added as a loose sheet to vol. VIII, while another loose sheet contains an example. These sheets are not mentioned in the table of contents of vol. VIII

Keywords: Infinite particle systems

Nature: Original

Retrieve article from Numdam

VII: 26, 284-290, LNM 321 (1973)

Relaxation in infinite spin systems (Statistical mechanics)

The existence of a stochastic process describing an infinitely many interacting particle system is proved

Comment: This is related to Sullivan,

Keywords: Interacting particle systems

Nature: Original

Retrieve article from Numdam

IX: 26, 471-485, LNM 465 (1975)

Multiplicative excessive measures and duality between equations of Boltzmann and of branching processes (Markov processes, Statistical mechanics)

The author investigates the connection between the branching Markov processes constructed over some given Markov processes and a non-linear equation close to Boltzmann's equation. A special class of excessive measures for the branching Markov process is described and studied, as well as the corresponding dual processes

Comment: For other contributions by the same author devoted to the relation between branching process and non-linear equations, see 618, 1011

Keywords: Boltzmann equation, Branching processes

Nature: Original

Retrieve article from Numdam

XXIX: 18, 194-201, LNM 1613 (1995)

Chaos multiplicatif : un traitement simple et complet de la fonction de partition (Statistical mechanics)

Introduced by Mandelbrot (

Keywords: Multiplicative chaos, Partition function, Pressure, Critical temperature

Nature: Original

Retrieve article from Numdam

XLIV: 18, 401-407, LNM 2046 (2012)

On the delocalized phase of the random pinning model (Statistical mechanics)

Keywords: Directed Polymer models, Partition function

Nature: Original