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    Уважаемые сотрудники ИТФ,<br>
    <br>
    На заседании Ученого совета в пятницу 2 ноября будет заслушан
    доклад:<br>
    <br>
    Victor Dotsenko<br>
    Two-temperature statistics of free energies in (1+1) directed
    polymers<br>
    <br>
    <div class="abstract tex">
      The joint statistical properties of two free energies computed at
      two different temperatures in the same sample of (1+1) directed
      polymers is studied in terms of the replica technique. The scaling
      dependence of the free energies differenceon the two temperatures
      <span class="MathJax" id="MathJax-Element-1-Frame" tabindex="0"
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                          style="display: inline-block; width: 0px;
                          height: 3.977em;"></span></span></span></span></span><span
                  style="display: inline-block; width: 0px; height:
                  0.994em;"></span></span></span><span style="display:
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    and <span class="MathJax" id="MathJax-Element-2-Frame" tabindex="0"
      style="position: relative;" data-mathml="<math
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      role="presentation"><nobr><span class="math" id="MathJax-Span-8"
          style="width: 0.927em; display: inline-block;"><span
            style="display: inline-block; position: relative; width:
            0.994em; height: 0px; font-size: 88%;"><span
              style="position: absolute; clip: rect(0.128em, 1000.99em,
              1.357em, -1000em); top: -0.994em; left: 0em;"><span
                class="mrow" id="MathJax-Span-9"><span class="msubsup"
                  id="MathJax-Span-10"><span style="display:
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                    height: 0px;"><span style="position: absolute; clip:
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                      -3.977em; left: 0em;"><span class="mi"
                        id="MathJax-Span-11" style="font-family:
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                          style="display: inline-block; overflow:
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                        style="display: inline-block; width: 0px;
                        height: 3.977em;"></span></span><span
                      style="position: absolute; top: -3.827em; left:
                      0.556em;"><span class="texatom"
                        id="MathJax-Span-12"><span class="mrow"
                          id="MathJax-Span-13"><span class="mn"
                            id="MathJax-Span-14" style="font-size:
                            70.7%; font-family: STIXGeneral;">2</span></span></span><span
                        style="display: inline-block; width: 0px;
                        height: 3.977em;"></span></span></span></span></span><span
                style="display: inline-block; width: 0px; height:
                0.994em;"></span></span></span><span style="display:
            inline-block; overflow: hidden; vertical-align: -0.194em;
            border-left: 0px solid; width: 0px; height: 0.832em;"></span></span></nobr></span>
    is derived. In particular, it is shown that if the two temperatures
    <span class="MathJax" id="MathJax-Element-3-Frame" tabindex="0"
      style="position: relative;" data-mathml="<math
xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>T</mi><mrow
class="MJX-TeXAtom-ORD"><mn>1</mn></mrow></msub><mo>&lt;</mo><msub><mi>T</mi><mrow
class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msub></math>"
      role="presentation"><nobr><span class="math" id="MathJax-Span-15"
          style="width: 2.915em; display: inline-block;"><span
            style="display: inline-block; position: relative; width:
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                  id="MathJax-Span-17"><span style="display:
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                            id="MathJax-Span-21" style="font-size:
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                        style="display: inline-block; width: 0px;
                        height: 3.977em;"></span></span></span></span><span
                  class="mo" id="MathJax-Span-22" style="font-family:
                  STIXGeneral; padding-left: 0.313em;"><</span><span
                  class="msubsup" id="MathJax-Span-23"
                  style="padding-left: 0.313em;"><span style="display:
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                    height: 0px;"><span style="position: absolute; clip:
                      rect(3.111em, 1000.63em, 4.19em, -1000em); top:
                      -3.977em; left: 0em;"><span class="mi"
                        id="MathJax-Span-24" style="font-family:
                        STIXGeneral; font-style: italic;">T<span
                          style="display: inline-block; overflow:
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                        style="display: inline-block; width: 0px;
                        height: 3.977em;"></span></span><span
                      style="position: absolute; top: -3.827em; left:
                      0.556em;"><span class="texatom"
                        id="MathJax-Span-25"><span class="mrow"
                          id="MathJax-Span-26"><span class="mn"
                            id="MathJax-Span-27" style="font-size:
                            70.7%; font-family: STIXGeneral;">2</span></span></span><span
                        style="display: inline-block; width: 0px;
                        height: 3.977em;"></span></span></span></span></span><span
                style="display: inline-block; width: 0px; height:
                2.557em;"></span></span></span><span style="display:
            inline-block; overflow: hidden; vertical-align: -0.194em;
            border-left: 0px solid; width: 0px; height: 0.832em;"></span></span></nobr></span>
    are close to each other the typical value of the fluctuating part of
    the free energies difference is proportional to <span
      class="MathJax" id="MathJax-Element-4-Frame" tabindex="0"
      style="position: relative;" data-mathml="<math
      xmlns="http://www.w3.org/1998/Math/MathML"><mo
stretchy="false">(</mo><mn>1</mn><mo>&#x2212;</mo><msub><mi>T</mi><mrow
class="MJX-TeXAtom-ORD"><mn>1</mn></mrow></msub><mrow
class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><msub><mi>T</mi><mrow
class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msub><msup><mo
      stretchy="false">)</mo><mrow
      class="MJX-TeXAtom-ORD"><mn>1</mn><mrow
class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mn>3</mn></mrow></msup></math>"
      role="presentation"><nobr><span class="math" id="MathJax-Span-28"
          style="width: 4.975em; display: inline-block;"><span
            style="display: inline-block; position: relative; width:
            5.611em; height: 0px; font-size: 88%;"><span
              style="position: absolute; clip: rect(1.503em, 1005.61em,
              2.947em, -1000em); top: -2.557em; left: 0em;"><span
                class="mrow" id="MathJax-Span-29"><span class="mo"
                  id="MathJax-Span-30" style="font-family: STIXGeneral;">(</span><span
                  class="mn" id="MathJax-Span-31" style="font-family:
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                  id="MathJax-Span-32" style="font-family: STIXGeneral;
                  padding-left: 0.25em;">−</span><span class="msubsup"
                  id="MathJax-Span-33" style="padding-left: 0.25em;"><span
                    style="display: inline-block; position: relative;
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                      -1000em); top: -3.977em; left: 0em;"><span
                        class="mi" id="MathJax-Span-34"
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                        italic;">T<span style="display: inline-block;
                          overflow: hidden; height: 1px; width:
                          0.077em;"></span></span><span style="display:
                        inline-block; width: 0px; height: 3.977em;"></span></span><span
                      style="position: absolute; top: -3.827em; left:
                      0.556em;"><span class="texatom"
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                          id="MathJax-Span-36"><span class="mn"
                            id="MathJax-Span-37" style="font-size:
                            70.7%; font-family: STIXGeneral;">1</span></span></span><span
                        style="display: inline-block; width: 0px;
                        height: 3.977em;"></span></span></span></span><span
                  class="texatom" id="MathJax-Span-38"><span
                    class="mrow" id="MathJax-Span-39"><span class="mo"
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                      STIXGeneral;">/</span></span></span><span
                  class="msubsup" id="MathJax-Span-41"><span
                    style="display: inline-block; position: relative;
                    width: 0.985em; height: 0px;"><span style="position:
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                        class="mi" id="MathJax-Span-42"
                        style="font-family: STIXGeneral; font-style:
                        italic;">T<span style="display: inline-block;
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                          0.077em;"></span></span><span style="display:
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                      style="position: absolute; top: -3.827em; left:
                      0.556em;"><span class="texatom"
                        id="MathJax-Span-43"><span class="mrow"
                          id="MathJax-Span-44"><span class="mn"
                            id="MathJax-Span-45" style="font-size:
                            70.7%; font-family: STIXGeneral;">2</span></span></span><span
                        style="display: inline-block; width: 0px;
                        height: 3.977em;"></span></span></span></span><span
                  class="msubsup" id="MathJax-Span-46"><span
                    style="display: inline-block; position: relative;
                    width: 1.312em; height: 0px;"><span style="position:
                      absolute; clip: rect(3.088em, 1000.29em, 4.367em,
                      -1000em); top: -3.977em; left: 0em;"><span
                        class="mo" id="MathJax-Span-47"
                        style="font-family: STIXGeneral;">)</span><span
                        style="display: inline-block; width: 0px;
                        height: 3.977em;"></span></span><span
                      style="position: absolute; top: -4.34em; left:
                      0.333em;"><span class="texatom"
                        id="MathJax-Span-48"><span class="mrow"
                          id="MathJax-Span-49"><span class="mn"
                            id="MathJax-Span-50" style="font-size:
                            70.7%; font-family: STIXGeneral;">1</span><span
                            class="texatom" id="MathJax-Span-51"><span
                              class="mrow" id="MathJax-Span-52"><span
                                class="mo" id="MathJax-Span-53"
                                style="font-size: 70.7%; font-family:
                                STIXGeneral;">/</span></span></span><span
                            class="mn" id="MathJax-Span-54"
                            style="font-size: 70.7%; font-family:
                            STIXGeneral;">3</span></span></span><span
                        style="display: inline-block; width: 0px;
                        height: 3.977em;"></span></span></span></span></span><span
                style="display: inline-block; width: 0px; height:
                2.557em;"></span></span></span><span style="display:
            inline-block; overflow: hidden; vertical-align: -0.218em;
            border-left: 0px solid; width: 0px; height: 1.021em;"></span></span></nobr></span>.
    It is also shown that the left tail asymptotics of this free energy
    difference probability distribution function coincides with the
    corresponding tail of the Tracy-Widom distribution.
    <br>
    Europhysics Letters, 116, 40004 (2016); arXiv:1703.04305
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